01/19/2005 CS267-Lecture 1 1

CS267/E233Applications of Parallel

Computers

Lecture 1: Introduction

James Demmel

demmel@cs.berkeley.edu

www.cs.berkeley.edu/~demmel/cs267_Spr05

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Outline

• Introduction

• Large important problems require powerful computers

• Why powerful computers must be parallel processors

• Why writing (fast) parallel programs is hard

• Principles of parallel computing performance

• Structure of the course

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Why we need powerful computers

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Units of Measure in HPC

• High Performance Computing (HPC) units are:- Flops: floating point operations

- Flops/s: floating point operations per second

- Bytes: size of data (a double precision floating point number is 8)

• Typical sizes are millions, billions, trillions…Mega Mflop/s = 106 flop/sec Mbyte = 220 = 1048576 ~ 106 bytes

Giga Gflop/s = 109 flop/sec Gbyte = 230 ~ 109 bytes

Tera Tflop/s = 1012 flop/sec Tbyte = 240 ~ 1012 bytes

Peta Pflop/s = 1015 flop/sec Pbyte = 250 ~ 1015 bytes

Exa Eflop/s = 1018 flop/sec Ebyte = 260 ~ 1018 bytes

Zetta Zflop/s = 1021 flop/sec Zbyte = 270 ~ 1021 bytes

Yotta Yflop/s = 1024 flop/sec Ybyte = 280 ~ 1024 bytes

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Simulation: The Third Pillar of Science

• Traditional scientific and engineering paradigm:1) Do theory or paper design.

2) Perform experiments or build system.

• Limitations:- 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 experimentation.

• Computational science paradigm:3) Use high performance computer systems to simulate the

phenomenon- Base on known physical laws and efficient numerical

methods.

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Some Particularly Challenging Computations• Science

- Global climate modeling- Biology: genomics; protein folding; drug design- Astrophysical modeling- Computational Chemistry- Computational Material Sciences and Nanosciences

• Engineering- Semiconductor design- Earthquake and structural modeling- Computation fluid dynamics (airplane design)- Combustion (engine design)- Crash simulation

• Business- Financial and economic modeling- Transaction processing, web services and search engines

• Defense- Nuclear weapons -- test by simulations- Cryptography

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Economic Impact of HPC

• Airlines:- System-wide logistics optimization systems on parallel systems.- Savings: approx. $100 million per airline per year.

• Automotive design:- Major automotive companies use large systems (500+ CPUs) for:

- CAD-CAM, crash testing, structural integrity and aerodynamics.

- One company has 500+ CPU parallel system.- Savings: approx. $1 billion per company per year.

• Semiconductor industry:- Semiconductor firms use large systems (500+ CPUs) for

- device electronics simulation and logic validation - Savings: approx. $1 billion per company per year.

• Securities industry:- Savings: approx. $15 billion per year for U.S. home mortgages.

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$5B World Market in Technical Computing

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1998 1999 2000 2001 2002 2003 Other

Technical Management andSupport

Simulation

Scientific Research and R&D

MechanicalDesign/Engineering Analysis

Mechanical Design andDrafting

Imaging

Geoscience and Geo-engineering

Electrical Design/EngineeringAnalysis

Economics/Financial

Digital Content Creation andDistribution

Classified Defense

Chemical Engineering

Biosciences

Source: IDC 2004, from NRC Future of Supercomputer Report

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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+t 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

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Global Climate Modeling Computation

• One piece is modeling the fluid flow in the atmosphere- Solve Navier-Stokes equations

- Roughly 100 Flops per grid point with 1 minute timestep

• Computational requirements:- To match real-time, need 5 x 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 8x to 16x

• 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

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A 1000 Year Climate Simulation

• 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/news/science/bigsplash2002.pdf

• 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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Climate Modeling on the Earth Simulator System

Development of ES started in 1997 in order to make a comprehensive understanding of global environmental changes such as global warming.

26.58Tflops was obtained by a global atmospheric circulation code.

35.86Tflops (87.5% of the peak performance) is achieved in the Linpack benchmark.

Its construction was completed at the end of February, 2002 and the practical operation started from March 1, 2002

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Astrophysics: Binary Black Hole Dynamics

• Massive supernova cores collapse to black holes. • At black hole center spacetime breaks down. • Critical test of theories of gravity –

General Relativity to Quantum Gravity. • Indirect observation – most galaxies

have a black hole at their center.• Gravity waves show black hole directly

including detailed parameters.• Binary black holes most powerful

sources of gravity waves. • Simulation extraordinarily complex –

evolution disrupts the spacetime !

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Heart Simulation

• Problem is to compute blood flow in the heart• Approach:

- Modeled as an elastic structure in an incompressible fluid.- The “immersed boundary method” due to Peskin and McQueen.- 20 years of development in model- Many applications other than the heart: blood clotting, inner ear,

paper making, embryo growth, and others- Use a regularly spaced mesh (set of points) for evaluating the fluid

• Uses- Current model can be used to design artificial heart valves- Can help in understand effects of disease (leaky valves)- Related projects look at the behavior of the heart during a heart

attack- Ultimately: real-time clinical work

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Heart Simulation Calculation

The involves solving Navier-Stokes equations- 64^3 was possible on Cray YMP, but 128^3 required for accurate model (would have taken 3 years).

- Done on a Cray C90 -- 100x faster and 100x more memory

- Until recently, limited to vector machines

- Needs more features:

- Electrical model of the heart, and details of muscles, E.g.,

- Chris Johnson

- Andrew McCulloch

- Lungs, circulatory systems

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Heart Simulation

Source: www.psc.org

Animation of lower portion of the heart

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Parallel Computing in Data Analysis

• Finding information amidst large quantities of data

• General themes of sifting through large, unstructured data sets:

- Has there been an outbreak of some medical condition in a community?

- Which doctors are most likely involved in fraudulent charging to medicare?

- When should white socks go on sale?

- What advertisements should be sent to you?

• Data collected and stored at enormous speeds (Gbyte/hour)

- remote sensor on a satellite

- telescope scanning the skies

- microarrays generating gene expression data

- scientific simulations generating terabytes of data

- NSA analysis of telecommunications

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Why powerful computers are

parallel

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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.

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Technology Trends: Microprocessor Capacity

2X transistors/Chip Every 1.5 years

Called “Moore’s Law”

Moore’s Law

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

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Impact of Device Shrinkage

• What happens when the feature size (transistor size) shrinks by a factor of x ?

• Clock rate goes up by x because wires are shorter

- actually less than x, because of power consumption

• 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

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Microprocessor Transistors per Chip

i4004

i80286

i80386

i8080

i8086

R3000R2000

R10000

Pentium

1,000

10,000

100,000

1,000,000

10,000,000

100,000,000

1970 1975 1980 1985 1990 1995 2000 2005

Year

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sist

ors

• Growth in transistors per chip • Increase in clock rate

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1970 1980 1990 2000

Year

Clo

ck R

ate

(MH

z)

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But there are limiting forces: Increased cost and difficulty of manufacturing

• Moore’s 2nd law (Rock’s law)

Demo of 0.06 micron CMOS

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More Limits: How fast can a serial computer be?

• Consider the 1 Tflop/s sequential machine:

- Data must travel some distance, r, to get from memory to CPU.

- To get 1 data element per cycle, this means 1012 times per second at the speed of light, c = 3x108 m/s. Thus r < c/1012 = 0.3 mm.

• Now put 1 Tbyte of storage in a 0.3 mm x 0.3 mm area:

- Each word occupies about 3 square Angstroms, or the size of a small atom.

• No choice but parallelism

r = 0.3 mm

1 Tflop/s, 1 Tbyte sequential machine

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Performance on Linpack Benchmark

System

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mean Rmax

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ASCI Red

Earth Simulator

ASCI White

Nov 2004: IBM Blue Gene L, 70.7 Tflops Rmax

Gflops

www.top500.org

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Why writing (fast) parallel programs is hard

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Principles of Parallel Computing

• Finding enough parallelism (Amdahl’s Law)

• Granularity

• Locality

• Load balance

• Coordination and synchronization

• Performance modeling

All of these things makes parallel programming even harder than sequential programming.

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“Automatic” Parallelism in Modern Machines• Bit level parallelism

- within floating point operations, etc.

• Instruction level parallelism (ILP)- 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

Limits to all of these -- for very high performance, need user to identify, schedule and coordinate parallel tasks

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Finding Enough Parallelism

• Suppose only part of an application seems parallel

• Amdahl’s law- let s be the fraction of work done sequentially, so

(1-s) is fraction parallelizable

- 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 may be limited by the sequential part

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Overhead of Parallelism

• Given enough parallel work, this is the biggest barrier to getting desired speedup

• Parallelism overheads include:- cost of starting a thread or process

- cost of communicating shared data

- cost of synchronizing

- extra (redundant) computation

• Each of these can be in the range of milliseconds (=millions of flops) on some systems

• Tradeoff: Algorithm needs sufficiently large units of work to run fast in parallel (I.e. large granularity), but not so large that there is not enough parallel work

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Locality and Parallelism

• Large memories are slow, fast memories are small

• Storage hierarchies are large and fast on average

• Parallel processors, collectively, have large, fast $- the slow accesses to “remote” data we call “communication”

• Algorithm should do most work on local data

ProcCache

L2 Cache

L3 Cache

Memory

Conventional Storage Hierarchy

ProcCache

L2 Cache

L3 Cache

Memory

ProcCache

L2 Cache

L3 Cache

Memory

potentialinterconnects

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Processor-DRAM Gap (latency)

µProc60%/yr.

DRAM7%/yr.

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“Moore’s Law”

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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

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MeasuringPerformance

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Improving Real Performance

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Peak Performance grows exponentially, a la Moore’s Law

In 1990’s, peak performance increased 100x; in 2000’s, it will increase 1000x

But efficiency (the performance relative to the hardware peak) has declined

was 40-50% on the vector supercomputers of 1990s

now as little as 5-10% on parallel supercomputers of today

Close the gap through ... Mathematical methods and algorithms that

achieve high performance on a single processor and scale to thousands of processors

More efficient programming models and tools for massively parallel supercomputers

PerformanceGap

Peak Performance

Real Performance

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Performance Levels

• Peak advertised performance (PAP)- You can’t possibly compute faster than this speed

• LINPACK - The “hello world” program for parallel computing

- Solve Ax=b using Gaussian Elimination, highly tuned

• Gordon Bell Prize winning applications performance- The right application/algorithm/platform combination plus years of work

• Average sustained applications performance- What one reasonable can expect for standard applications

When reporting performance results, these levels are often confused, even in reviewed publications

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Performance on Linpack Benchmark

System

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Rmax

max Rmax

mean Rmax

min Rmax

ASCI Red

Earth Simulator

ASCI White

Nov 2004: IBM Blue Gene L, 70.7 Tflops Rmax

Gflops

www.top500.org

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Performance Levels (for example on NERSC-3)

• Peak advertised performance (PAP): 5 Tflop/s

• LINPACK (TPP): 3.05 Tflop/s

• Gordon Bell Prize winning applications performance : 2.46 Tflop/s

- Material Science application at SC01

• Average sustained applications performance: ~0.4 Tflop/s

- Less than 10% peak!

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Course Organization

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Who is in the class?

• This class is listed as both a CS and Engineering class

• Normally a mix of CS, EE, and other engineering and science students

• This class seems to be about:- 40% CS

- 15% EE

- 45% Other (Bio, Civil, Mechanical, Math…)

• For final projects we encourage interdisciplinary teams- This is the way parallel scientific software is generally built

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First Assignment• See home page for details.• Find an application of parallel computing and build a web

page describing it.- Choose something from your research area.- Or from the web or elsewhere.

• Create a web page describing the application. - Describe the application and provide a reference (or link)- Describe the platform where this application was run- Find peak and LINPACK performance for the platform and its rank on

the TOP500 list- Find performance of your selected application- What ratio of sustained to peak performance is reported?- Evaluate project: How did the application scale, I.e. was speed roughly

proportional to the number of processorsh? What were the major difficulties in obtaining good performance? What tools and algorithms were used?

• Send us (Jim and Yozo) the link (we will publish a list online)

• Due next week, Wednesday (1/26)

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Rough Schedule of Topics• Introduction

• Parallel Programming Models and Machines- Shared Memory and Multithreading

- Distributed Memory and Message Passing

- Data parallelism

• Sources of Parallelism in Simulation

• Tools - Languages (UPC)

- Performance Tools

- Visualization

- Environments

• Algorithms- Dense Linear Algebra

- Partial Differential Equations (PDEs)

- Particle methods

- Load balancing, synchronization techniques

- Sparse matrices

• Applications: biology, climate, combustion, astrophysics

• Project Reports

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Reading Materials• Some on-line texts:

- Demmel’s notes from CS267 Spring 1999, which are similar to 2000 and 2001. However, they contain links to html notes from 1996.

- http://www.cs.berkeley.edu/~demmel/cs267_Spr99/

- Simon’s notes from Fall

- http://www.nersc.gov/~simon/cs267/

- Ian Foster’s book, “Designing and Building Parallel Programming”.

- http://www-unix.mcs.anl.gov/dbpp/

• Potentially useful texts:- “Sourcebook for Parallel Computing”, by Dongarra, Foster, Fox, ..

- A general overview of parallel computing methods

- “Performance Optimization of Numerically Intensive Codes” by Stefan Goedecker and Adolfy Hoisie

- This is a practical guide to optimization, mostly for those of you who have never done any optimization

• Reports on Supercomputing (see web page)

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Requirements• Fill out on-line account request for Millennium machine.

- See course web page for pointer

• Fill out class survey- Handout in class, or see course web page for pointer

• Build a web page- Every week or two students will report explorations, ideas, proposed

work, and work to the TA via an organized webpage- There will be 3-4 programming assignments geared towards hands-on

experience, interdisciplinary teams.- There will be a Final Project

- Teams of 2-3, interdisciplinary is best.- Interesting applications or advance of systems.- Presentation (poster session)- Conference quality paper

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What you should get out of the course

In depth understanding of:

• When is parallel computing useful?

• Understanding of parallel computing hardware options.

• Overview of programming models (software) and tools.

• Some important parallel applications and the algorithms

• Performance analysis and tuning

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Administrative Information

• Instructors:- Jim Demmel, 737 Soda, demmel@cs.berkeley.edu

- TA:Yozo Hida, 515 Soda, yozo@cs.berkeley.edu

• Accounts – fill out forms- Submit online form for Millennium account

- See web page for pointer:

- NERSC account forms will be available later from Yozo

• Lecture notes are based on previous semester notes:- Jim Demmel, David Culler, David Bailey, Bob Lucas, Kathy Yelick

and Horst Simon

• Most class material and lecture notes are at: - http://www.cs.berkeley.edu/~demmel/cs267_Spr05

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Extra slides

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Transaction Processing

• Parallelism is natural in relational operators: select, join, etc.

• Many difficult issues: data partitioning, locking, threading.

(mar. 15, 1996)

0

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Thro

ughput

(tp

mC

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other

Tandem Himalaya

IBM PowerPC

DEC Alpha

SGI PowerChallenge

HP PA

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SIA Projections for Microprocessors

Compute power ~1/(Feature Size)3

0.01

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20

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atu

re S

ize

(m

icro

ns

) &

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ion

T

ran

sis

tors

pe

r c

hip

Feature Size(microns)

Transistors perchip x 106

based on F.S.Preston, 1997

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Much of the Performance is from Parallelism

Name

Bit-LevelParallelism

Instruction-LevelParallelism

Thread-LevelParallelism?