Metrics

1
Metrics

• FLOPS (FLoating point Operations Per Sec) - a
  measure of the numerical processing of a CPU
  which can be an indicator of its scientific
  computing capability.
• The floating-point format is a variation of
  scientific notation - the real number is
  represented using a mantissa, base, and exponent
• Storing real number in computers
• use the fixed length of word as the storage space
  for a real number (e.g. 64bits)
• Mantissa is normalised (1.61 is normalised, 16.1
  is not)
• The mantissa and exponents are converted to
  base-2
• Some parts of the word are used to store the
  mantissa, 1bit to store sign, and the rest to
  store the exponent
• Advantages and disadvantages
• Using a fixed-length space to store a wide
  overall range of values
• If 64 bits are used to store the real numbers,
  in which 11 bits are used to store exponent and
  52 bits to mantissa (the remaining 1 bit used to
  store sign). We can derive the range of numbers
  this storage layout can represent
• More bits are used to store mantissa, higher
  precision, but smaller range
• More bits are used to store exponent, wider
  range, but lower precision
• The difference between two successive numbers is
  not uniform
• When the numbers cannot be perfected converted to
  base-2 numbers, they must be rounded to be stored
  in the format, leading to some problems where
  algebraic rules do not appear to apply
• The LINPACK benchmark produces a FLOPS results.
  This solves a dense system of linear equations by
  Gaussian elimination.

2
Example of Floating Point Numbers

• 172.625 base 10
• 10101100.101 X 20 base 2
• 1.0101100101 X 27 base 2 normalised
• Using 32 bit (4 bytes) to store the number in
  computers, in which 1 bit for sign, 8 bits for
  exponent, and the rest for Mantissa
• 0 00000111 00000000000010101100101
• S Exp Mantissa

3
Metrics

• MIPS (Millions of Instructions Per Second) - a
  measure of the speed of a processor.
• Peak MIPS rates (usually vendor supplied) can be
  misrepresentative
• Meaningless Information on Performance for
  Salespeople
• People seldom refer to it

4
Metrics

• SPECint - measures a processors integer
  processing capabilities.
• Latest version SPECint2006
• Can test cpu, memory, compiler, but cannot test
  networking, I/O
• Consists of a series of benchmarks (12, including
  compression, compilation)
• each benchmark has a reference time
• Dividing the measured runtime of the benchmark by
  the reference time and multiplying by 100
  provides a base ratio
• For example, if we run the benchmark 401.bzip2 to
  test the system, whose reference time is 1400.
  The actual runtime of the benchmark is 140 sec.
  then the base ratio is calculated as
  1400/1401001000
• These are averaged to produce a final performance
  figure for the processor.

5
SPECint2006 benchmark suite
Benchmark Language Category
400.perlbench C Programming Language
401.bzip2 C Compression
403.gcc C C Compiler
429.mcf C Combinatorial Optimization
445.gobmk C Artificial Intelligence
456.hmmer C Search Gene Sequence
458.sjeng C Artificial Intelligence
462.libquantum C Physics / Quantum Computing
464.h264ref C Video Compression
471.omnetpp C Discrete Event Simulation
473.astar C Path-finding Algorithms
483.xalancbmk C XML Processing
6
Metrics

• Communication
• Bandwidth (bytes/sec)
• How much data can be sent per second over the
  network
• Latency (seconds)
• The time between one processor sending a message
  and the other processor receiving the message
• Interconnection type On-board interconnection or
  over networks.
• Topologies bus, crossbar, hub, switch
• Protocols stacks
• unicast, multicast, broadcast.
• Storage capabilities
• Storage facilities register, cache, memory, hard
  disk
• Bandwidth and Latency.
• Bandwidth how much data can be accessed per
  second in a certain storage facility
• Latency the time between sending a data
  accessing request and receiving the requested
  data
• Memory hierarchies (cpu register-gt cache -gt main
  memory -gt remote memory)
• Local, remote file systems

7
Top500 Supercomputer list

• Website www.top500.org
• Top500 project Started in 1993, updated twice a
  year
• Aiming to track the trend in HPC
• Using LINPACK to measure the performance (FLOPS)
• Essentially, LINPACK is to solve the dense system
  of linear equations Axb (commonly encountered in
  engineering area)
• Users are allowed to change the problem size to
  get the maximum performance, which is used to
  rank the supercomputers
• Theoretical peak performance is also given for
  reference

8
Top500 Supercomputer list

• Tends to represent parallel computers, so
  distributed systems such as SETI_at_Home are
  neglected.
• Does not consider storage or I/O issues
• Both custom designed machines and commodity
  machines win positions in the list
• General trend towards commodity machines (COTS -
  Commodity Off-The-Shelf). BlueGene/L, however, is
  not a COTS machine
• Connecting a large number of machines with
  relatively lower performance is more rewarding
  than connecting a small number of machines each
  with high performance
• Read the paper A note on the Zipf distribution
  of Top500 supercomputers (download from my
  homepage)
• Performance doubles each year, better than
  Moores Law.
• Moores Law performance doubles approximately
  every 18 months
• Dominated by the United States (location map of
  the Top100 machines http//www.top500.org/lists/2
  006/11/top100map)
• UK supercomputers in the list
• Cambridge No.20 (http//www.top500.org/system/826
  7 ),
• AWE No. 15

9
Top Machine

• BlueGene/L
• first supercomputer in the Blue Gene project
• Specialised systems based on the Power
  architecture.
• Individual power 400 processors at 700Mhz
• Two processors reside in a single chip.
• Two chips reside on a compute card with 512MB
  memory.
• 16 of these compute cards are placed on a node
  board.
• 32 node boards fit into one cabinet, and there
  are 64 cabinets.
• 130,712 CPUs with theoretical peak of 183.5
  TFLOPS/s
• Multiple network topologies available, which can
  be selected depending on the application.
• High density of processors in a small area
• Low power and (comparatively) slow processors -
  just lots of them!
• Fast interconnects and low-latency.