1 friday, october 06, 2006 measure twice, cut once. -carpenter’s motto

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Friday, October 06, 2006

Measure twice, cut once.

- Carpenter’s Motto

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Sources of overhead

Inter-process communicationIdlingReplicated computation

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Sources of overhead

Inter-process communicationIdlingReplicated computation

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Ts: The original single-processor serial time. Tis: The additional serial time spent on average for

• Inter-processor communications• Setup• Depends on N.

Tp: The original single-processor parallelizable time. Tip: The additional time spent on average by each

processor • Setup• Idle time

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Simplified expression

S(N) = Ts + Tp

Ts+ N*Tis + Tp/N + Tip

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1 20 40 60 80 100 120 140

N (Processors)

SN

) S

pe

ed

up Tp=10

Tp=100

Tp=1000

Tp=10000

Tp=100000

Linear

Ts=10, Tip=1, Tis=0

Communication time negligible compared to computation. What you would expect from Amdahl’s law alone.

Straight line reference for linear speedup

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120.00

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1 20 40 60 80 100 120 140

N (Processors)

SN

) S

pe

ed

up Tp=10

Tp=100

Tp=1000

Tp=10000

Tp=100000

Linear

Ts=10, Tip=1, Tis=10

Adding small serial time. Adding more processors results in lower speedup.

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0.00

20.00

40.00

60.00

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100.00

120.00

140.00

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1 20 40 60 80 100 120 140

N (Processors)

SN

) S

pe

ed

up Tp=10

Tp=100

Tp=1000

Tp=10000

Tp=100000

Linear

Ts=10, Tip=1, Tis=1

Quadratic N dependence, e.g. every processor speaks to all others.

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Adding processors won’t provide additional speedup unless the problem is scaled up as well.

Should not distribute calculations with small Tp/Tis over a large number of processors.

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Scaling a problem

Does number of tasks scale with the problem size?

Increase in problem size should increase the number of tasks rather than the size of individual tasks. Should be able to solve larger

problems when more processors are available.

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What can we tell from our observations?

We implemented an algorithm on parallel computer X and achieved a speedup of 10.8 on 12 processors with problem size N=100 .

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What can we tell from our observations?

We implemented an algorithm on parallel computer X and achieved a speedup of 10.8 on 12 processors with problem size N=100 .

Region of observation is too narrow.What if N=10 or N=1000?

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What can we tell from our observations?

T is the execution time, P is number of processors and N is problem size

T= N + N2/PT= (N + N2)/P + 100T= (N + N2)/P + 0.6 P2

All these algorithms all achieve a speedup of about 10.8 when P=12 and N=100 .

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Addition example

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Addition example

Speedup :Ratio of time taken to solve a problem on a

single processor to time required to solve it on a parallel computer with p identical processing elements

Speedup for addition example?

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Speedup :Comparison with best known serial

algorithm

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Efficiency :

Fraction of time which a processor spends doing useful work.

E = S/p

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Cost :Product of parallel runtime and the number of processors.

Cost: pTp (Note: Tp here stands to the parallel runtime. The time from the moment the parallel computation starts to the moment last processing element finishes execution)

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Cost optimal :

If cost of solving a problem on a parallel computer has same asymptotic growth as a function of input size as the fastest known sequential algorithm on a single processor.

Cost for addition example: O(n logn)

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Cost optimal :If cost of solving a problem on a parallel computer has same asymptotic growth as a function of input size as the fastest known sequential algorithm on a single processor.

Cost for addition example: O(n logn)Not cost optimal.

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Effect of non-cost-optimality

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If overhead increases sub-linearly with respect to problem size.

Keep efficiency fixed by increasing both the problem size and number of processors

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Keep efficiency fixed by increasing both the problem size and number of processors

Scalable parallel systems

Ability to utilize increasing processing elements effectively

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Scalability and cost-optimality are related

Scalable system can always be made cost-optimal if number of processing elements and size of problem are chosen carefully

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Scalability and cost-optimality are related

Scalable system can always be made cost-optimal if number of processing elements and size of problem are chosen carefully

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Speedup that is greater than linear: Super-linear

Speedup Anomalies

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Cache effects. Each processor has a small amount of cache When a problem is executed on a greater number of

processors, more of its data can be placed in cache and as a result, total computation time will tend to decrease.

If reduction in computation time due to this cache effect offsets increases in communication and idle time from use of additional processors then super-linearity results.

Similarly, the increased physical memory available in a multiprocessor may reduce the cost of memory accesses by avoiding the need for virtual memory paging.

Speedup Anomalies

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Search anomalies.

If a search tree contains solutions at varying depths, then multiple depth-first searches will, on average, explore fewer tree nodes before finding a solution than will a sequential depth-first search.

Speedup Anomalies

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Message Passing

Partitioned address spaceData explicitly decomposed and placed by

programmerLocality of access.Cooperation for send receive operations.Structured and static requirements

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Message Passing

Most message passing programs are written using SPMD

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Message Passing

The need for a standard.

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The Message Passing Interface (MPI) standard is the de-facto industry standard for parallel applications. Designed by leading industry and academic

researchers

MPI Library that is widely used to parallelize

scientific and compute-intensive programs

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LAM (Indiana University), MPICH (Argonne National Laboratory, Chicago) are popular open source implementations of MPI library.

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Implementations of MPI (such as LAM, MPICH) provide an API of library calls that allow users to pass messages between nodes of a parallel application.

Run on a wide variety of systems, from desktop workstations, clusters to large supercomputers (and everything in between).

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MPI: the Message Passing Interface

The minimal set of MPI routines.

MPI_Init Initializes MPI.

MPI_Finalize Terminates MPI. MPI_Comm_size Determines the number of processes. MPI_Comm_rank Determines the label of calling process. MPI_Send Sends a message.

MPI_Recv Receives a message.

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Starting and Terminating the MPI Library MPI_Init is called prior to any calls to other MPI routines. Its

purpose is to initialize the MPI environment. MPI_Finalize is called at the end of the computation, and it

performs various clean-up tasks to terminate the MPI environment. The prototypes of these two functions are:

int MPI_Init(int *argc, char ***argv)

int MPI_Finalize() MPI_Init also strips off any MPI related command-line

arguments. All MPI routines, data-types, and constants are prefixed by “MPI_”.

The return code for successful completion is MPI_SUCCESS. (mpi.h)

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Hello World MPI Program#include <stdio.h>#include <mpi.h>int main(int argc, char *argv[]){ int rank, size; MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &rank); MPI_Comm_size(MPI_COMM_WORLD, &size); printf("Hello, world! I am %d of %d\n", rank, size); MPI_Finalize(); return 0;}

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LAM

Before any MPI programs can be executed, the LAM run-time environment must be launched. This is typically called “booting LAM.”

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LAM

Before any MPI programs can be executed, the LAM run-time environment must be launched. This is typically called “booting LAM.”

A text file is required that lists the hosts on which to launch the LAM run-time environment. This file is typically referred to as a “boot schema”, “hostfile”, or “machinefile.”

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Sample machinefile

hpcc.lums.edu.pk

compute-0-0.local

compute-0-1.local

compute-0-2.local

compute-0-3.local

compute-0-4.local

compute-0-5.local

compute-0-6.local

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LAM

Settings have been done on your accounts and the following files have been copied in your home directory.

ssh_scriptmachinefilehellompi.c

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First time commands

(Logout of all old sessions and re-login)

source ssh_script

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First time commandssource ssh_script Warning: Permanently added 'compute-0-0.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-1.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-2.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-3.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-4.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-5.local' (RSA) to the list of known hosts./bin/bashWarning: Permanently added 'compute-0-6.local' (RSA) to the list of known hosts./bin/bash

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First time commands

source ssh_script /bin/bash/bin/bash/bin/bash/bin/bash/bin/bash/bin/bash/bin/bash

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First time commandslamboot -v machinefileLAM 7.1.1/MPI 2 C++/ROMIO - Indiana Universityn-1<13857> ssi:boot:base:linear: booting n0 (hpcc.lums.edu.pk)n-1<13857> ssi:boot:base:linear: booting n1 (compute-0-0.local)n-1<13857> ssi:boot:base:linear: booting n2 (compute-0-1.local)n-1<13857> ssi:boot:base:linear: booting n3 (compute-0-2.local)n-1<13857> ssi:boot:base:linear: booting n4 (compute-0-3.local)n-1<13857> ssi:boot:base:linear: booting n5 (compute-0-4.local)n-1<13857> ssi:boot:base:linear: booting n6 (compute-0-5.local)n-1<13857> ssi:boot:base:linear: booting n7 (compute-0-6.local)n-1<13857> ssi:boot:base:linear: finished

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First time commands

lamnodesn0 hpcc.lums.edu.pk:1:origin,this_noden1 compute-0-0.local:1:n2 compute-0-1.local:1:n3 compute-0-2.local:1:n4 compute-0-3.local:1:n5 compute-0-4.local:1:n6 compute-0-5.local:1:n7 compute-0-6.local:1:

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First time commands

mpicc hellompi.c -o hello

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First time commands

mpirun -np 8 hello

Hello, world! I am 0 of 8

Hello, world! I am 4 of 8

Hello, world! I am 2 of 8

Hello, world! I am 6 of 8

Hello, world! I am 3 of 8

Hello, world! I am 5 of 8

Hello, world! I am 7 of 8

Hello, world! I am 1 of 8

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First time commandslamhaltLAM 7.1.1/MPI 2 C++/ROMIO - Indiana University

lamwipe machinefileLAM 7.1.1/MPI 2 C++/ROMIO - Indiana University

lamnodes-----------------------------------------------------------------------------It seems that there is no lamd running on the host hpcc.lums.edu.pk.This indicates that the LAM/MPI runtime environment is not operating.The LAM/MPI runtime environment is necessary for the "lamnodes" command.Please run the "lamboot" command the start the LAM/MPI runtimeenvironment. See the LAM/MPI documentation for how to invoke"lamboot" across multiple machines.

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Sequence whenever you want to run an MPI program

1. Compile using mpicc

2. Start LAM runtime environment using lamboot

3. Run MPI program using mpirun

4. When you are done, shut down LAM universe using lamhalt and lamwipe

5. lamclean can be useful if a parallel job crashes to remove all running programs