Introducción a la computación de altas prestaciones



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  • Francisco Almeida y Francisco de Sande
  • Departamento de Estadística, I.O. y Computación
  • Universidad de La Laguna
  • La Laguna, 12 de febrero de 2004
  • Questions
  • Why Parallel Computers?
  • How Can the Quality of the Algorithms be Analyzed?
  • How Should Parallel Computers Be Programmed?
  • Why the Message Passing Programming Paradigm?
  • Why de Shared Memory Programming Paradigm?

Introduction to Parallel Computing

  • OUTLINE
  • Introduction to Parallel Computing
  • Performance Metrics
  • Models of Parallel Computers
  • The MPI Message Passing Library
  • Examples
  • The OpenMP Shared Memory Library
  • Examples

Applications Demanding more Computational Power:

  • Why Parallel Computers ?
  • Applications Demanding more Computational Power:
    • Artificial Intelligence
    • Weather Prediction
    • Biosphere Modeling
    • Processing of Large Amounts of Data (from sources such as satellites)
    • Combinatorial Optimization
    • Image Processing
    • Neural Network
    • Speech Recognition
    • Natural Language Understanding
    • etc..
  • Cost
  • Performance
  • 1960 s
  • 1970 s
  • 1980 s
  • 1990 s
  • SUPERCOMPUTERS

Top500

  • www.top500.org

Performace Metrics

Speed-up

  • Ts = Sequential Run Time: Time elapsed between the begining and the end of its execution on a sequential computer.
  • Tp = Parallel Run Time: Time that elapses from the moment that a parallel computation starts to the moment that the last processor finishes the execution.
  • Speed-up: T*s / Tp ? p
  • T*s = Time of the best sequential algorithm to solve the problem.

Speed-up

Speed-up

Speed-up

Speed-up

Efficiency

  • In practice, ideal behavior of an speed-up equal to p is not achieved because while executing a parallel algorithm, the processing elements cannot devote 100% of their time to the computations of the algorithm.
  • Efficiency: Measure of the fraction of time for which a processing element is usefully employed.
  • E = (Speed-up / p) x 100 %

Efficiency

Amdahl`s Law

  • Amdahl`s law attempt to give a maximum bound for speed-up from the nature of the algorithm chosen for the parallel implementation.
  • Seq = Proportion of time the algorithm needs to be spent in purely sequential parts.
  • Par = Proportion of time that might be done in parallel
  • Seq + Par = 1 (where 1 is for algebraic simplicity)
  • Maximum Speed-up = (Seq + Par) / (Seq + Par / p) = 1 / (Seq + Par / p)
  • %
  • Seq
  • Par
  • Maximum
  • Speed-up
  • 0,1
  • 0,001
  • 0,999
  • 500,25
  • 0,5
  • 0,005
  • 0,995
  • 166,81
  • 1
  • 0,01
  • 0,99
  • 90,99
  • 10
  • 0,1
  • 0,9
  • 9,91
  • p = 1000

Example

  • A problem to be solved many times over several different inputs.
    • Evaluate F(x,y,z)
      • x in {1 , ..., 20}; y in {1 , ..., 10}; z in {1 , ..., 3};
    • The total number of evaluations is 20*10*3 = 600.
    • The cost to evaluate F in one point (x, y, z) is t.
    • The total running time is t * 600.
    • If t is equal to 3 hours.
      • The total running time for the 600 evaluations is 1800 hours  75 days

Speed-up

Models

The Sequential Model

  • RAM
  • Von Neumann
  • The RAM model express computations on von Neumann architectures.
  • The von Neumann architecture is universally accepted for sequential computations.

The Parallel Model

  • PRAM
  • BSP, LogP
  • PVM, MPI, HPF, Threads, OPenMP
  • Parallel Architectures
  • Computational Models
  • Programming Models
  • Architectural Models

Digital AlphaServer 8400

  • Hardware
  • C4-CEPBA
  • 10 Alpha processors21164
  • 2 Gb Memory
  • 8,8 Gflop/s
  • Shared Memory
  • BusTopology

SGI Origin 2000

  • Hardware
  • C4-CEPBA
  • 64 R1000 processos
  • 8 Gb memory
  • 32 Gflop/s

The SGI Origin 3000 Architecture (1/2)

    • jen50.ciemat.es
    • 160 processors MIPS R14000 / 600MHz
    • On 40 nodes with 4 processors each
    • Data and instruction cache on-chip
    • Irix Operating System
    • Hypercubic Network


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