Transcript Slide - UCSB Computer Science

CS 240A
Applied Parallel Computing
John R. Gilbert
[email protected]
http://www.cs.ucsb.edu/~cs240a
Thanks to Kathy Yelick and Jim Demmel at UCB for some of their slides.
Course bureacracy
• Read course home page
http://www.cs.ucsb.edu/~cs240a/homepage.html
• Join Google discussion group (see course home page)
• Accounts on Triton, San Diego Supercomputing Center:
• Use “ssh –keygen –t rsa” and then email your “id_rsa.pub” file to
Stefan Boeriu, [email protected]
• If you weren’t signed up for the course as of last week, email me
your registration info right away
• Triton logon demo & tool intro coming soon– watch
Google group for details
Homework 1
• See course 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 the performance of your selected application
• What ratio of sustained to peak performance is reported?
• Evaluate the project: How did the application scale, ie was speed
roughly proportional to the number of processors? What were the
major difficulties in obtaining good performance? What tools and
algorithms were used?
• Send us (John and Hans) the link (we will post them)
• Due next Monday, April 5
Two examples of big parallel problems
• Bone density modeling:
• Physical simulation
• Lots of numerical computing
• Spatially local
• Vertex betweenness centrality:
• Exploring an unstructured graph
• Lots of pointer-chasing
• Little numerical computing
• No spatial locality
Social newtork analysis
Betweenness Centrality (BC)
CB(v): Among all the shortest
paths, what fraction of them pass
through the node of interest?
A typical software stack for an
application enabled with the
Combinatorial BLAS
Brandes’ algorithm
Betweenness Centrality using
Sparse GEMM
1

4
3
AT
X
.
(ATX) *¬X
• Parallel breadth-first search is implemented with
sparse matrix-matrix multiplication
• Work efficient algorithm for BC
2
7
6
5
BC performance in distributed memory
Millions
TEPS score
BC performance
250
Input: RMAT scale N
2N vertices
Average degree 8
200
150
Scale 17
Scale 18
100
Scale 19
50
Scale 20
25
36
49
64
81
100
121
144
169
196
225
256
289
324
361
400
441
484
0
Number of Cores
• TEPS: Traversed Edges Per Second
• Batch of 512 vertices at each iteration
• Code only a few lines longer than Matlab version
Pure MPI-1 version.
No reliance on any
particular hardware
Parallel Computers Today
Two Nvidia
8800 GPUs
> 1 TFLOPS
Oak Ridge / Cray Jaguar
> 1.75 PFLOPS
 TFLOPS = 1012 floating point ops/sec
 PFLOPS = 1,000,000,000,000,000 / sec
(1015)
Intel 80core chip
> 1 TFLOPS
AMD Opteron quad-core die
Cray XMT
(highly multithreaded
shared memory)
1
2
i =n
.
.
.
3
i =2
i =1
Programs
running in
parallel
i =n
Subproblem
A
i =3
4
.
Su bproblem
B
.
.
i =1
Serial
Code
i =0
Concurrent
threads of
computation
Subproblem A
....
Hardware
stream s
(128)
Unused streams
Instruction
Ready
Pool;
Pipeline of
executing
instructions
• Top 500 List
• http://www.top500.org/list/2009/11/100
The Computer Architecture Challenge
 Most high-performance
computer designs allocate
resources to optimize
Gaussian elimination on
large, dense matrices.
 Originally, because linear
algebra is the middleware of
scientific computing.
 Nowadays, mostly for
bragging rights.
P A
=
L
x
U
Why are powerful
computers parallel?
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
Scaling microprocessors
• What happens when feature size shrinks by a factor of x?
• Clock rate used to go up by x , but no longer
• Clock rates are topping out due to power (heat) limits
• Transistors per unit area goes up by x2
• Die size also tends to increase
• Typically another factor of ~x
• Raw computing capability of the chip goes up by ~ x3 !
• But it’s all for parallelism, not speed
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
“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?
Generic Parallel Machine Architecture
Storage
Hierarchy
Proc
Cache
L2 Cache
Proc
Cache
L2 Cache
Proc
Cache
L2 Cache
L3 Cache
L3 Cache
Memory
Memory
Memory
potential
interconnects
L3 Cache
• Key architecture question: Where is the interconnect, and how fast?
• Key algorithm question: Where is the data?