Transcript Support-Graph Preconditioning

CSE 260
Parallel Computation
Allan Snavely, Henri Casanova
[email protected]
[email protected]
http://www.sdsc.edu/~allans/cs260/cs260.htm
Outline
• Introductions
• Why we need powerful computers
• Why powerful computers are parallel
• Issues in parallel performance
• Parallel computers, yesterday and today
• Class organization
Introductions
• Instructors: Allan Snavely, [email protected],
www.sdsc.edu/~allans Henri Casanova,
[email protected], www.cs.ucsd.edu/~casanova/
• T.A.: Michael McCracken, [email protected]
• Course web page:
http://www.sdsc.edu/~allans/cs260/cs260.htm
• HPCS experiment: more at end of class today.
Thanks to Kathy Yelick and Jim Demmel , and John Gilbert at UCB for some of these slides.
Why do we need
powerful computers?
Simulation: The Third Pillar of Science
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Traditional scientific and engineering paradigm:
1) Do theory or paper design.
2) Perform experiments or build system.
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Limitations:
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Too difficult -- build large wind tunnels.
Too expensive -- build a throw-away passenger jet.
Too slow -- wait for climate or galactic evolution.
Too dangerous -- weapons, drug design, climate experiments.
Computational science paradigm:
3) Use high performance computer systems to simulate the
phenomenon.
• Base on known physical laws and efficient numerical methods.
Some Challenging Computations
• Science
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Global climate modeling
Astrophysical modeling
Biology: genomics; protein folding; drug design
Computational Chemistry
Computational Material Sciences and Nanosciences
• Engineering
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Crash simulation
Semiconductor design
Earthquake and structural modeling
Computation fluid dynamics (airplane design)
Combustion (engine design)
• Business
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Financial and economic modeling
Transaction processing, web services and search engines
• Defense
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Nuclear weapons -- test by simulation
Cryptography
Units of Measure in HPC
• High Performance Computing (HPC) units are:
• Flops: floating point operations
• Flop/s: floating point operations per second
• Bytes: size of data (double precision floating point number is 8)
• Typical sizes are millions, billions, trillions…
Mega
Mflop/s = 106 flop/sec
Giga
Gflop/s = 109 flop/sec
Tera
Tflop/s = 1012 flop/sec
Peta
Pflop/s = 1015 flop/sec
Exa
Eflop/s = 1018 flop/sec
Mbyte = 106 byte
(also 220 = 1048576)
Gbyte = 109 byte
(also 230 = 1073741824)
Tbyte = 1012 byte
(also 240 = 10995211627776)
Pbyte = 1015 byte
(also 250 = 1125899906842624)
Ebyte = 1018 byte
Global Climate Modeling Problem
• Problem is to compute:
f(latitude, longitude, elevation, time) 
temperature, pressure, humidity, wind velocity
• Approach:
• Discretize the domain, e.g., a measurement point every 10 km
• Devise an algorithm to predict weather at time t+1 given t
• Uses:
- Predict major events,
e.g., El Nino
- Use in setting air
emissions standards
Source: http://www.epm.ornl.gov/chammp/chammp.html
Global Climate Modeling Computation
• One piece is modeling the fluid flow in the atmosphere
• Solve Navier-Stokes problem
• Roughly 100 Flops per grid point with 1 minute timestep
• Computational requirements:
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To match real-time, need 5x 1011 flops in 60 seconds = 8 Gflop/s
Weather prediction (7 days in 24 hours)  56 Gflop/s
Climate prediction (50 years in 30 days)  4.8 Tflop/s
To use in policy negotiations (50 years in 12 hours)  288 Tflop/s
• To double the grid resolution, computation is at least 8x
• State of the art models require integration of
atmosphere, ocean, sea-ice, land models, plus
possibly carbon cycle, geochemistry and more
• Current models are coarser than this
High Resolution
Climate Modeling on
NERSC-3 – P. Duffy,
et al., LLNL
A 1000 Year Climate Simulation
• Demonstration of the
Community Climate Model
(CCSM2)
• A 1000-year simulation
shows long-term, stable
representation of the
earth’s climate.
• 760,000 processor hours
used
• Temperature change
shown
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Warren Washington and Jerry Meehl, National Center for Atmospheric
Research; Bert Semtner, Naval Postgraduate School; John Weatherly,
U.S. Army Cold Regions Research and Engineering Lab Laboratory et
al.
http://www.nersc.gov/aboutnersc/pubs/bigsplash.pdf
Climate Modeling on the Earth Simulator System
 Development of ES started in 1997 with the goal of enabling
a comprehensive understanding of global environmental
changes such as global warming.
 Construction was completed February, 2002 and practical
operation started March 1, 2002
 35.86 Tflops (87.5% of peak performance) on Linpack benchmark.
 26.58 Tflops on a global atmospheric circulation code.
Why are powerful
computers parallel?
Tunnel Vision by Experts
• “I think there is a world market for maybe five
computers.”
• Thomas Watson, chairman of IBM, 1943.
• “There is no reason for any individual to have a
computer in their home”
• Ken Olson, president and founder of Digital Equipment Corporation, 1977.
• “640K [of memory] ought to be enough for anybody.”
• Bill Gates, chairman of Microsoft,1981.
Slide source: Warfield et al.
Technology Trends: Microprocessor Capacity
Moore’s Law
Moore’s Law: #transistors/chip
doubles every 1.5 years
Microprocessors have
become smaller, denser,
and more powerful.
Gordon Moore (co-founder of
Intel) predicted in 1965 that the
transistor density of
semiconductor chips would
double roughly every 18
months.
Slide source: Jack Dongarra
How fast can a serial computer be?
1 Tflop 1 TB
sequential
machine
r = .3 mm
• Consider the 1 Tflop sequential machine
• data must travel some distance, r, to get from memory to CPU
• to get 1 data element per cycle, this means 10^12 times per
second at the speed of light, c = 3e8 m/s
• so r < c/10^12 = .3 mm
• Now put 1 TB of storage in a .3 mm^2 area
• each word occupies ~ 3 Angstroms^2, the size of a small atom
Scaling microprocessors
• What happens when feature size shrinks by a factor of x?
• Clock rate goes up by x
• actually a little less
• Transistors per unit area goes up by x2
• Die size also tends to increase
• typically another factor of ~x
• Raw computing power of the chip goes up by ~ x4 !
• of which x3 is devoted either to parallelism or locality
“Automatic” Parallelism in Modern Machines
• Bit level parallelism
• within floating point operations, etc.
• Instruction level parallelism
• multiple instructions execute per clock cycle
• Memory system parallelism
• overlap of memory operations with computation
• OS parallelism
• multiple jobs run in parallel on commodity SMPs
There are limits to all of these -- for very high performance,
user must identify, schedule and coordinate parallel tasks
Number of transistors per processor chip
100,000,000
10,000,000
Transistors
R10000
Pentium
1,000,000
i80386
i80286
100,000
R3000
R2000
i8086
10,000
i8080
i4004
1,000
1970 1975 1980 1985 1990 1995 2000 2005
Year
Number of transistors per processor chip
100,000,000
10,000,000
Instruction-Level
Parallelism
Transistors
R10000
Pentium
1,000,000
i80386
i80286
100,000
R3000
R2000
i8086
10,000
i8080
i4004
1,000
1970 1975 1980 1985 1990 1995 2000 2005
Year
Bit-Level
Parallelism
Thread-Level
Parallelism?
Issues in parallel
performance
Locality and Parallelism
Conventional
Storage
Proc
Hierarchy
Cache
L2 Cache
Proc
Cache
L2 Cache
Proc
Cache
L2 Cache
L3 Cache
L3 Cache
Memory
Memory
Memory
• Large memories are slow, fast memories are small
• Storage hierarchies are large and fast on average
• Parallel processors, collectively, have large, fast cache
• the slow accesses to “remote” data we call “communication”
• Algorithm should do most work on local data
potential
interconnects
L3 Cache
Finding Enough Parallelism: Amdahl’s Law
• Suppose only part of an application seems parallel
• Amdahl’s law
• Let s be the fraction of work done sequentially,
so (1-s) is the fraction parallelizable
• Let P = number of processors
Speedup(P) = Time(1)/Time(P)
<= 1/(s + (1-s)/P)
<= 1/s
• Even if the parallel part speeds up perfectly, the
sequential part limits overall performance.
Load Imbalance
• Load imbalance is the time that some processors in the
system are idle due to
• insufficient parallelism (during that phase)
• unequal size tasks
• Examples of the latter
• adapting to “interesting parts of a domain”
• tree-structured computations
• fundamentally unstructured problems
• Algorithm needs to balance load
Parallel computers,
yesterday and today
• Dead supercomputers
• Top 500 list
• Flashmob computing (!?)
Parallel Computing Today
Japanese Earth Simulator machine
Small class Beowulf cluster
Course organization
Course overview
• Key ideas:
• Algorithms
• Programming models
• Performance
• Course outline – see home page
Resources
• Course home page:
http://www.sdsc.edu/~allans/cs260/cs260.htm
• Computing resources:
• 128-multi-streaming processor (MSP) Cray X1 with 512 GB of
memory and 21 terabytes of disk. The X1, named Klondike at
Arctic Region Supercomputing Center (ARSC)
• 1632 processor IBM Power4 SP: DataStar (SDSC)
• Return the course questionnaire so we can create accounts!
• No textbook – see course homepage for references
Requirements
• Four 2-week homework assignments
• First one is assigned today!!!!!
• Individual effort
• 40% of course grade
• Final project
• Significant parallel programming project
• Teams of three
• Teams should be interdisciplinary
(this is how real parallel software is built)
• 50% of course grade
• Scribe notes for one lecture
• Due one week after lecture
• Sign up for a day to scribe
• 10% of course grade for scribing and class participation