computational grids. computational problems problems that have lots of computations and usually lots...

Computational Grids

Computational Problems

• Problems that have lots of computations and usually lots of data.

Demand for Computational Speed

• Continual demand for greater computational speed from a computer system than is currently possible

• Areas requiring great computational speed include numerical modeling and simulation of scientific and engineering problems.

• Computations must be completed within a “reasonable” time period.

Grand Challenge Problems

One that cannot be solved in a reasonable amount of time with today’s computers. Obviously, an execution time of 10 years is always unreasonable.

Examples

• Modeling large DNA structures• Global weather forecasting• Modeling motion of astronomical bodies.

Weather Forecasting

• Atmosphere modeled by dividing it into 3-dimensional cells.

• Calculations of each cell repeated many times to model passage of time.

Global Weather Forecasting Example• Suppose whole global atmosphere divided into cells of size

1 mile 1 mile 1 mile to a height of 10 miles (10 cells high) - about 5 108 cells.

• Suppose each calculation requires 200 floating point operations. In one time step, 1011 floating point operations necessary.

• To forecast the weather over 7 days using 1-minute intervals, a computer operating at 1Gflops (109 floating point operations/s) takes 106 seconds or over 10 days.

• To perform calculation in 5 minutes requires computer operating at 3.4 Tflops (3.4 1012 floating point operations/sec).

Modeling Motion of Astronomical Bodies

• Each body attracted to each other body by gravitational forces. Movement of each body predicted by calculating total force on each body.

• With N bodies, N - 1 forces to calculate for each

body, or approx. N2 calculations. (N log2 N for an efficient approx. algorithm.)

• After determining new positions of bodies, calculations repeated.

• A galaxy might have, say, 1011 stars.

• Even if each calculation done in 1 ms (extremely optimistic figure), it takes 109 years for one iteration using N2 algorithm

and

almost a year for one iteration using an efficient N log2 N approximate algorithm.

Astrophysical N-body simulation by Scott Linssen (undergraduate UNC-Charlotte student).

High Performance Computing (HPC)

• Traditionally, achieved by using the multiple computers together - parallel computing.

• Simple idea! -- Using multiple computers (or processors) simultaneously should be able can solve the problem faster than a single computer.

High Performance Computing

• Long History:– Multiprocessor system of various

types (1950’s onwards)

– Supercomputers (1960s-80’s)

– Cluster computing (1990’s)

– Grid computing (2000’s) ??Maybe, but let’s first look at how to achieve HPC.

Speedup Factor

where ts is execution time on a single processor and tp is execution time on a multiprocessor.

S(p) gives increase in speed by using multiprocessor.

Use best sequential algorithm with single processor system. Underlying algorithm for parallel implementation might be (and is usually) different.

S(p) = Execution time using one processor (best sequential algorithm)

Execution time using a multiprocessor with p processors

ts

tp

=

Maximum Speedup

Maximum speedup is usually p with p processors (linear speedup).

Possible to get superlinear speedup (greater than p) but usually a specific reason such as:

• Extra memory in multiprocessor system• Nondeterministic algorithm

Maximum Speedup Amdahl’s law

Serial section Parallelizable sections

(a) One processor

(b) Multipleprocessors

fts (1 - f)ts

ts

(1 - f)ts/ptp

p processors

Speedup factor is given by:

This equation is known as Amdahl’s law

S(p) ts p

fts (1 f )ts /p 1 (p 1)f

Speedup against number of processors

4

8

12

16

20

4 8 12 16 20

f = 20%

f = 10%

f = 5%

f = 0%

Number of processors, p

Speedup factor, S(p)

Even with infinite number of processors, maximum speedup limited to 1/f.

ExampleWith only 5% of computation being serial, maximum speedup is 20, irrespective of number of processors.

Superlinear SpeedupExample - Searching

(a) Searching each sub-space sequentially

t s

t s/p

Start Time

t

Solution foundx ts /p

Sub-space

search

x indeterminate

(b) Searching each sub-space in parallel

Solution found

t

Question

What is the speed-up now?

Speed-up then given by

S(p)x

tsp

t+

t=

Worst case for sequential search when solution found in last sub-space search.Then parallel version offers greatest benefit, i.e.

S(p)

p 1–p

ts t+

t=

  as t tends to zero

Least advantage for parallel version when solution found in first sub-space search of the sequential search, i.e.

Actual speed-up depends upon which subspace holds solution but could be extremely large.

S(p) = tt

= 1

Computing Platforms for Parallel Programming

Types of Parallel Computers

Two principal types:

1. Single computer containing multiple processors - main memory is shared, hence called “Shared memory multiprocessor”

2. Interconnected multiple computer systems

Conventional ComputerConsists of a processor executing a program stored in a (main) memory:

Each main memory location located by its address. Addresses start at 0 and extend to 2b - 1 when there are b bits (binary digits) in address.

Main memory

Processor

Instructions (to processor)Data (to or from processor)

Shared Memory Multiprocessor• Extend single processor model - multiple

processors connected to a single shared memory with a single address space:

Memory

Processors

A real system will have cache memory associated with each processor

Examples

• Dual Pentiums

• Quad Pentiums

Quad Pentium Shared Memory MultiprocessorProcessor

L2 Cache

Bus interface

L1 cache

Processor

L2 Cache

Bus interface

L1 cache

Processor

L2 Cache

Bus interface

L1 cache

Processor

L2 Cache

Bus interface

L1 cache

Memory controller

Memory

I/O interface

I/O bus

Processor/memorybus

Shared memory

Programming Shared Memory Multiprocessors

• Threads - programmer decomposes program into parallel sequences (threads), each being able to access variables declared outside threads.

Example: Pthreads

• Use sequential programming language with preprocessor compiler directives, constructs, or syntax to declare shared variables and specify parallelism. Examples: OpenMP (an industry standard), UPC

(Unified Parallel C) -- needs compilers.

• Parallel programming language with syntax to express parallelism. Compiler creates executable code -- not now common.

• Use parallelizing compiler to convert regular sequential language programs into parallel executable code - also not now common.

Message-Passing Multicomputer

Complete computers connected through an interconnection network:

Processor

Interconnectionnetwork

Local

Computers

Messages

memory

Dedicated cluster with a master node

UserExternal network

Master node

Compute nodes

Switch

2nd Ethernet interface

Ethernet interface

Cluster

UNC-C’s cluster used for grid course(Department of Computer Science)

P P

M

P P

M

P P

M

P P

M

coit-grid01 coit-grid02 coit-grid03 coit-grid04

3.4 GHz dual Xeon Pentiums

To External network Switch

Funding for this cluster provided by the University of North Carolina, Office of the President, specificially for the grid computing course.

Programming Clusters

• Usually based upon explicit message-passing.

• Common approach -- a set of user-level libraries for message passing. Example:– Parallel Virtual Machine (PVM) - late 1980’s.

Became very popular in mid 1990’s. – Message-Passing Interface (MPI) - standard

defined in 1990’s and now dominant.

MPI(Message Passing Interface)

• Message passing library standard developed by group of academics and industrial partners to foster more widespread use and portability.

• Defines routines, not implementation.

• Several free implementations exist.

MPI designed:

• To address some problems with earlier message-passing system such as PVM.

• To provide powerful message-passing mechanism and routines - over 126 routines(although it is said that one can write reasonable MPI

programs with just 6 MPI routines).

Message-Passing Programming using User-level Message Passing Libraries

Two primary mechanisms needed:

1. A method of creating separate processes for execution on different computers

2. A method of sending and receiving messages

Multiple program, multiple data (MPMD) model

Sourcefile

Executable

Processor 0 Processor p - 1

Compile to suitprocessor

Sourcefile

Single Program Multiple Data (SPMD) model.

Basic MPI way

Sourcefile

Executables

Processor 0 Processor p - 1

Compile to suitprocessor

Different processes merged into one program. Control statements select different parts for each processor to execute.

Multiple Program Multiple Data (MPMD) Model

Process 1

Process 2spawn();

Time

Start executionof process 2

Separate programs for each processor. One processor executes master process. Other processes started from within master process - dynamic process creation.

Can be done with MPI version 2

Communicators• Defines scope of a communication operation.

• Processes have ranks associated with communicator.

• Initially, all processes enrolled in a “universe” called MPI_COMM_WORLD, and each process is given a unique rank, a number from 0 to p - 1, with p processes.

• Other communicators can be established for groups of processes.

Using SPMD Computational Model

main (int argc, char *argv[]) {MPI_Init(&argc, &argv);

.

.MPI_Comm_rank(MPI_COMM_WORLD,&myrank); /*find rank */

if (myrank == 0)master();

elseslave();..

MPI_Finalize();}

where master() and slave() are to be executed by master process and slave process, respectively.

Basic “point-to-point”Send and Receive Routines

Process 1 Process 2

send(&x, 2);

recv(&y, 1);

x y

Movementof data

Generic syntax (actual formats later)

Passing a message between processes using send() and recv() library calls:

Message Tag

• Used to differentiate between different types of messages being sent.

• Message tag is carried within message.

• If special type matching is not required, a wild card message tag is used, so that the recv() will match with any send().

Message Tag Example

Process 1 Process 2

send(&x,2, 5);

recv(&y,1, 5);

x y

Movementof data

Waits for a message from process 1 with a tag of 5

To send a message, x, with message tag 5 from a source process, 1, to a destination process, 2, and assign to y:

Synchronous Message Passing

Routines return when message transfer completed.

Synchronous send routine• Waits until complete message can be accepted by

the receiving process before sending the message.

Synchronous receive routine• Waits until the message it is expecting arrives.

Synchronous send() and recv() using 3-way protocol

Process 1 Process 2

send();

recv();Suspend

Time

processAcknowledgment

MessageBoth processescontinue

(a) When send() occurs before recv()

Request to send

Synchronous send() and recv() using 3-way protocol

Process 1 Process 2

recv();

send();Suspend

Time

process

Acknowledgment

MessageBoth processescontinue

(b) When recv() occurs before send()

Request to send

• Synchronous routines intrinsically perform two actions:– They transfer data and – They synchronize processes.

Asynchronous Message Passing

• Routines that do not wait for actions to complete before returning. Usually require local storage for messages.

• More than one version depending upon the actual semantics for returning.

• In general, they do not synchronize processes but allow processes to move forward sooner. Must be used with care.

MPI Blocking and Non-Blocking

• Blocking - return after their local actions complete, though the message transfer may not have been completed.

• Non-blocking - return immediately. Assumes that data storage used for transfer not modified by subsequent statements prior to being used for transfer, and it is left to the programmer to ensure this.

These terms may have different interpretations in other systems.

How message-passing routines return before message transfer completed

Process 1 Process 2

send();

recv();

Message buffer

Readmessage buffer

Continueprocess

Time

Message buffer needed between source and destination to hold message:

Asynchronous routines changing to synchronous routines

• Buffers only of finite length and a point could be reached when send routine held up because all available buffer space exhausted.

• Then, send routine will wait until storage becomes re-available - i.e then routine behaves as a synchronous routine.

Parameters of MPI blocking send

MPI_Send(buf, count, datatype, dest, tag, comm)

Address of send buffer

Number of items to send

Datatype of each item

Rank of destination process

Message tag

Communicator

Parameters of MPI blocking receive

MPI_Recv(buf,count,datatype,dest,tag,comm,status)

Address of receive buffer Max. number of

items to receive

Datatype of each item

Rank of source process

Message tag

Communicator

Status after operation

Example

To send an integer x from process 0 to process 1,

MPI_Comm_rank(MPI_COMM_WORLD,&myrank); /* find rank */

if (myrank == 0) {int x;MPI_Send(&x,1,MPI_INT,1,msgtag,MPI_COMM_WORLD);

} else if (myrank == 1) {int x;MPI_Recv(&x,1,MPI_INT,0,msgtag,MPI_COMM_WORLD,status);

}

MPI Nonblocking Routines

• Nonblocking send - MPI_Isend() - will return “immediately” even before source location is safe to be altered.

• Nonblocking receive - MPI_Irecv() - will return even if no message to accept.

Detecting when message receive if sent with non-blocking send routine

Completion detected by MPI_Wait() and MPI_Test().

MPI_Wait() waits until operation completed and returns then.

MPI_Test() returns with flag set indicating whether operation completed at that time.

Need to know which particular send you are waiting for.

Identified with request parameter.

Example

To send an integer x from process 0 to process 1 and allow process 0 to continue,

MPI_Comm_rank(MPI_COMM_WORLD, &myrank);/* find rank */if (myrank == 0) {

int x;MPI_Isend(&x,1,MPI_INT,1,msgtag,MPI_COMM_WORLD, req1);compute();MPI_Wait(req1, status);

} else if (myrank == 1) {int x;MPI_Recv(&x,1,MPI_INT,0,msgtag, MPI_COMM_WORLD, status);

}

“Group” message passing routines

Have routines that send message(s) to a group of processes or receive message(s) from a group of processes

Higher efficiency than separate point-to-point routines although not absolutely necessary.

BroadcastSending same message to a group of processes.(Sometimes “Multicast” - sending same message to defined group of processes, “Broadcast” - to all processes.)

MPI_bcast();

buf

MPI_bcast();

data

MPI_bcast();

datadata

Process 0 Process p - 1Process 1

Action

Code

MPI form

MPI Broadcast routine

int MPI_Bcast(void *buf, int count, MPI_Datatype datatype, int root, MPI_Comm comm)

Actions:Broadcasts message from root process to all processes in comm and itself.

Parameters:*buf message buffercount number of entries in bufferdatatype data type of bufferroot rank of root

Scatter

MPI_scatter();

buf

MPI_scatter();

data

MPI_scatter();

datadata

Process 0 Process p - 1Process 1

Action

Code

MPI form

Sending each element of an array in root process to a separate process. Contents of ith location of array sent to ith process.

Gather

MPI_gather();

buf

MPI_gather();

data

MPI_gather();

datadata

Process 0 Process p - 1Process 1

Action

Code

MPI form

Having one process collect individual values from set of processes.

Reduce

MPI_reduce();

buf

MPI_reduce();

data

MPI_reduce();

datadata

Process 0 Process p - 1Process 1

+

Action

Code

MPI form

Gather operation combined with specified arithmetic/logical operation.

Example: Values could be gathered and then added together by root:

Collective Communication

Involves set of processes, defined by an intra-communicator. Message tags not present. Principal collective operations:

• MPI_Bcast() - Broadcast from root to all other processes• MPI_Gather() - Gather values for group of processes• MPI_Scatter() - Scatters buffer in parts to group of processes• MPI_Alltoall() - Sends data from all processes to all

processes• MPI_Reduce() - Combine values on all processes to single

value• MPI_Reduce_scatter() - Combine values and scatter results• MPI_Scan() - Compute prefix reductions of data on processes

ExampleTo gather items from group of processes into process 0, using dynamically allocated memory in root process:

int data[10];/*data to be gathered from processes*/

MPI_Comm_rank(MPI_COMM_WORLD, &myrank);/* find rank */if (myrank == 0) {MPI_Comm_size(MPI_COMM_WORLD,&grp_size);/*find size*/

/*allocate memory*/buf = (int *)malloc(grp_size*10*sizeof (int));

}MPI_Gather(data,10,MPI_INT,buf,grp_size*10,MPI_INT,0, MPI_COMM_WORLD);

MPI_Gather() gathers from all processes, including root.

Sample MPI program

#include “mpi.h”#include <stdio.h>#include <math.h>#define MAXSIZE 1000void main(int argc, char *argv) {

int myid, numprocs;int data[MAXSIZE], i, x, low, high, myresult, result;char fn[255];char *fp;MPI_Init(&argc,&argv);MPI_Comm_size(MPI_COMM_WORLD,&numprocs);MPI_Comm_rank(MPI_COMM_WORLD,&myid);if (myid == 0) { /* Open input file and initialize data */

strcpy(fn,getenv(“HOME”));strcat(fn,”/MPI/rand_data.txt”);if ((fp = fopen(fn,”r”)) == NULL) {

printf(“Can’t open the input file: %s\n\n”, fn);exit(1);

}for(i = 0; i < MAXSIZE; i++) fscanf(fp,”%d”, &data[i]);

}MPI_Bcast(data, MAXSIZE, MPI_INT, 0, MPI_COMM_WORLD); /* broadcast data */x = n/nproc; /* Add my portion Of data */low = myid * x;high = low + x;for(i = low; i < high; i++)

myresult += data[i];printf(“I got %d from %d\n”, myresult, myid); /* Compute global sum */MPI_Reduce(&myresult, &result, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);if (myid == 0) printf(“The sum is %d.\n”, result);MPI_Finalize();

}

Debugging/Evaluating Parallel Programs Empirically

Visualization ToolsPrograms can be watched as they are executed in a space-time diagram (or process-time diagram):

Process 1

Process 2

Process 3

TimeComputingWaitingMessage-passing system routine

Message

Visualization tools available for MPI. An example - Upshot

Evaluating Programs EmpiricallyMeasuring Execution Time

To measure the execution time between point L1 and point L2 in the code, we might have a construction such as

.

t1 = MPI_Wtime(); /* start */..

t2 = MPI_Wtime(); /* end */.

elapsed_time = t2 - t1); /*elapsed_time */printf(“Elapsed time = %5.2f seconds”, elapsed_time);

MPI provides the routine MPI_Wtime() for returning time (in seconds).

Executing MPI programs

• MPI version 1 standard does not address implementation and did not specify how programs are to be started and each implementation has its own way.

Compiling/Executing MPI Programs

Basics

For MPICH, use two commands:

• mpicc to compile a program

• mirun to execute program

mpicc

Example

mpicc –o hello hello.c

compiles hello.c to create the executable hello.

mpicc is (probably) a script calling cc and hence all regular cc flags can be attached.

mpirun

Example

mpirun –np 3 hello

executes 3 instances of hello on the local machine (when using MPICH).

Using multiple computersFirst create a file (say called “machines”) containing list of computers you what to use.

Examplecoit-1grid01.uncc.educoit-2grid01.uncc.educoit-3grid01.uncc.educoit-4grid01.uncc.edu

Then specify machines file in mpirun command:

Example

mpirun –np 3 -machinefile machines hello

executes 3 instances of hello using the computers listed in the file. (Scheduling will be round-robin unless otherwise specified.)

MPI-2

• The MPI standard, version 2 does recommend a command for starting MPI programs, namely:

mpiexec -n # prog

where # is the number of processes and prog is the program.

Sample MPI Programs

Hello WorldPrinting out rank of process

#include "mpi.h"#include <stdio.h>int main(int argc,char *argv[]) {

int myrank, numprocs;MPI_Init(&argc, &argv);MPI_Comm_rank(MPI_COMM_WORLD,&myrank);MPI_Comm_size(MPI_COMM_WORLD,&numprocs)printf("Hello World from process %d of %d\n", myrank, numprocs);MPI_Finalize();return 0;

}

Question

Suppose this program is compiled as helloworld and is executed on a single computer with the command:

mpirun -np 4 helloworld

What would the output be?

Answer

Several possible outputs depending upon order processes are executed.

ExampleHello World from process 2 of 4Hello World from process 0 of 4Hello World form process 1 of 4Hello World form process 3 of 4

Adding communication to get process 0 to print all messages:#include "mpi.h"#include <stdio.h>int main(int argc,char *argv[]) {

int myrank, numprocs;char greeting[80]; /* message sent from slaves to master */

MPI_Status status;MPI_Init(&argc, &argv);MPI_Comm_rank(MPI_COMM_WORLD,&myrank);MPI_Comm_size(MPI_COMM_WORLD,&numprocs);sprintf(greeting,"Hello World from process %d of %d\n",rank,size);if (myrank == 0 ) { /* I am going print out everything */ printf("s\n",greeting); /* print greeting from proc 0 */ for (i = 1; i < numprocs; i++) { /* greetings in order */

MPI_Recv(geeting,sizeof(greeting),MPI_CHAR,i,1,MPI_COMM_WORLD, &status);printf(%s\n", greeting);

}} else {

MPI_Send(greeting,strlen(greeting)+1,MPI_CHAR,0,1, MPI_COMM_WORLD);

}MPI_Finalize();return 0;

}

MPI_Get_processor_name()

Return name of processor executing code (and length of string). Arguments:

MPI_Get_processor_name(char *name,int *resultlen)

Example int namelen; char procname[MPI_MAX_PROCESSOR_NAME];

MPI_Get_processor_name(procname,&namelen);

returned in here

Easy then to add name in greeting with:

sprintf(greeting,"Hello World from process %d of %d on $s\n", rank, size, procname);

Pinging processes and timingMaster-slave structure

#include <mpi.h>void master(void); void slave(void);int main(int argc, char **argv){ int myrank; printf("This is my ping program\n"); MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &myrank); if (myrank == 0) { master(); } else { slave(); } MPI_Finalize(); return 0;}

Master routinevoid master(void){

int x = 9;double starttime, endtime;MPI_Status status;printf("I am the master - Send me a message when you receive this number %d\n", x);starttime = MPI_Wtime();MPI_Send(&x,1,MPI_INT,1,1,MPI_COMM_WORLD);MPI_Recv(&x,1,MPI_INT,1,1,MPI_COMM_WORLD,&status);endtime = MPI_Wtime();printf("I am the master. I got this back %d \n", x);printf("That took %f seconds\n",endtime - starttime);

}

Slave routinevoid slave(void){

int x;MPI_Status status;printf("I am the slave - working\n");MPI_Recv(&x,1,MPI_INT,0,1,MPI_COMM_WORLD,&status);printf("I am the slave. I got this %d \n", x);MPI_Send(&x, 1, MPI_INT, 0, 1, MPI_COMM_WORLD);

}

Example using collective routines

MPI_Bcast()

MPI_Reduce()

Adding numbers in a file.

#include “mpi.h”#include <stdio.h>#include <math.h>#define MAXSIZE 1000void main(int argc, char *argv){

int myid, numprocs;int data[MAXSIZE], i, x, low, high, myresult, result;char fn[255];char *fp;MPI_Init(&argc,&argv);MPI_Comm_size(MPI_COMM_WORLD,&numprocs);MPI_Comm_rank(MPI_COMM_WORLD,&myid);if (myid == 0) { /* Open input file and initialize data */

strcpy(fn,getenv(“HOME”));strcat(fn,”/MPI/rand_data.txt”);if ((fp = fopen(fn,”r”)) == NULL) {

printf(“Can’t open the input file: %s\n\n”, fn);exit(1);

}for(i = 0; i < MAXSIZE; i++) fscanf(fp,”%d”, &data[i]);

}MPI_Bcast(data, MAXSIZE, MPI_INT, 0, MPI_COMM_WORLD); /* broadcast data */x = n/nproc; /* Add my portion Of data */low = myid * x;high = low + x;for(i = low; i < high; i++)

myresult += data[i];printf(“I got %d from %d\n”, myresult, myid); /* Compute global sum */MPI_Reduce(&myresult, &result, 1, MPI_INT, MPI_SUM, 0, MPI_COMM_WORLD);if (myid == 0) printf(“The sum is %d.\n”, result);MPI_Finalize();

}

C Program Command Line Arguments

A normal C program specifies command line arguments to be passed to main with:

int main(int argc, char *argv[])

where• argc is the argument count and • argv[] is an array of character pointers.

– First entry is a pointer to program name– Subsequent entries point to subsequent strings

on the command line.

MPIC program command line arguments

• Implementations of MPI remove from the argv array any command line arguments used by the implementation.

• Note MPI_Init requires argc and argv (specified as addresses)

ExampleGetting Command Line Argument

#include “mpi.h”#include <stdio.h>int main (int argc, char *argv[]) {int n;

/* get and convert character string argument to integer value /*

n = atoi(argv[1]);

return 0;}

Executing MPI program with command line arguments

mpirun -np 2 myProg 56 123

argv[1] argv[2]

Remember these array elements hold pointers to the arguments.

argv[0]

Removed by MPI - probably

by MPI_Init()

More Information on MPI

• Books: “Using MPI Portable Parallel Programming with the Message-Passing Interface 2nd ed.,” W. Gropp, E. Lusk, and A. Skjellum, The MIT Press,1999.

• MPICH: http://www.mcs.anl.gov/mpi

• LAM MPI: http://www.lam-mpi.org

Parallel Programming Home Page

http://www.cs.uncc.edu/par_prog

Gives step-by-step instructions for compiling and executing programs, and other information.

Grid-enabled MPI

Several versions of MPI developed for a grid:

• MPICH-G, MPICH-G2

• PACXMPI

MPICH-G2 is based on MPICH and uses Globus.

MPI code for the grid

No difference in code from regular MPI code.

Key aspect is MPI implementation:

• Communication methods

• Resource management

Communication Methods

• Implementation should take into account whether messages are between processor on the same computer or processors on different computers on the network.

• Pack messages into less larger message, even if this requires more computations

MPICH-G2

• Complete implementation of MPI

• Can use existing MPI programs on a grid without change

• Uses Globus to start tasks, etc.

• Version 2 a complete redesign from MPICH-G for Globus 2.2 or later.

Compiling Application Program

As with regular MPI programs, compile on each machine you intend to use and make accessible to computers.

Running an MPICH-G2 Programmpirun

• submits a Globus RSL script (Resource Specification Language Script) to launch application

• RSL script can be created by mpirun or you can write your own.

• RSL script gives powerful mechanism to specify different executables etc., but low level.

mpirun(with it constructing RSL script)

• Use if want to launch a single executable on binary compatible machines with a shared file system.

• Requires a “machines” file - a list of computers to be used (and job managers)

“Machines” file

• Computers listed by their Globus job manager service followed by optional maximum number of node (tasks) on that machine.

• If job manager omitted (i.e., just name of computer), will default to Globus job manager.

Location of “machines” file

• mpirun command expects the “machines” file either in– the directory specified by -machinefile flag

– the current directory used to execute the mpirun command, or

– in <MPICH_INSTALL_PATH>/bin/machines

Running MPI program

• Uses the same command line as a regular MPI program:

mpirun -np 25 my_prog

creates 25 tasks allocated on machines in “machines’ file in around robin fashion.

ExampleWith the machines file containing:

“coit-0grid01.uncc.edu” 4“coit-grid02.uncc.edu” 5

and the command:

mpirun -np 10 myProg

the first 4 processes (jobs) would run on coit-grid01, the next 5 on coit-grid02, and the remaining one on coit-grid01.

mpirunwith your own RSL script

• Necessary if machines not executing same executable.

• Easiest way to create script is to modify existing one.

• Use mpirun –dumprsl– Causes script printed out. Application program

not launched.

Example

mpirun -dumprsl -np 2 myprog

will generate appropriate printout of an rsl document according to the details of the job from the command line and machine file.

Given rsl file, myRSL.rsl, use:

mpirun -globusrsl myRSL.rsl

to submit modified script.

MPICH-G2 internals

• Processes allocated a “machine-local” number and a “grid global” number - translated into where process actually resides.

• Non-local operations uses grid services• Local operations do not.• globusrun command submits

simultaneous job requests

Limitations

• “machines” file limits computers to those known - no discovery of resources

• If machines heterogeneous, need appropriate executables available, and RSL script

• Speed an issue - original version MPI-G slow.

More information on MPICH-G2

http://www.niu.edu/mpi

http://www.globus.org/mpi

http://www.hpclab.niu.edu/mpi/g2_body.htm

Parallel Programming Techniques

Suitable for a Grid

Message-Passing on a Grid

• VERY expensive, sending data across network costs millions of cycles

• Bandwidth shared with other users

• Links unreliable

Computational Strategies

• As a computing platform, a grid favors situations with absolute minimum communication between computers.

StrategiesWith no/minimum communication:

• “Embarrassingly Parallel” Computations– those computations which obviously can be

divided into parallel independent parts. Parts executed on separate computers.

• Separate instance of the same problem executing on each system, each using different data

Embarrassingly Parallel Computations

A computation that can obviously be divided into a number of completely independent parts, each of which can be executed by a separate process(or).

Processes

Results

Input data

No communication or very little communication between processes.Each process can do its tasks without any interaction with other processes

Monte Carlo Methods

• An embarrassingly parallel computation.

• Monte Carlo methods use of random selections.

Simple Example: To calculate Circle formed within a square, with radius of 1. Square has sides 2 2.

Area =

Total area = 4

2

2

Ratio of area of circle to square given by

Area of circle = (1)2 = Area of square 2 x 2 4

• Points within square chosen randomly.• Score kept of how many points happen to

lie within circle.• Fraction of points within circle will be /4,

given a sufficient number of randomly selected samples.

Method actually computes an integral.

One quadrant of the construction can be described by integral

1 x2– xd01

4---=

x

1

f(x)

1

1

y 1 x2–=

So can use method to compute any integral!

Monte Carlo method very useful if the function cannot be integrated numerically (maybe having a large number of variables).

Alternative (better) “Monte Carlo” Method Use random values of x to compute f (x) and sum values of f (x)

where xr are randomly generated values of x between x1 and x2.

y

x

Area f(x) xdx1

x2 1

N----

N lim f( xr)r

i 1=

N= = (x2 – x1)

X1X2

ExampleComputing the integral

Sequential Code

sum = 0;for (i = 0; i < N; i++) { /* N random samples */

xr = rand_v(x1, x2); /* next random value */sum = sum + xr * xr - 3 * xr /* compute f(xr)*/

}area = (sum / N) * (x2 - x1);

randv(x1, x2) returns pseudorandom number between x1 and x2.

x1

x2 (x2 – 3x) dx

For parallelizing Monte Carlo code, must address best way to generate random numbers in parallel.

Can use SPRNG (Scalable Pseudo-random Number Generator) -- supposed to be a good parallel random number generator.

Executing separate problem instances

In some application areas, same program executed repeatedly - ideal if with different parameters (“parameter sweep”)

Nimrod/G -- a grid broker project that targets parameter sweep problems.

Techniques to reduce effects of network communication

• Latency hiding with communication/computation overlap

• Better to have fewer larger messages than many smaller ones

Synchronous Algorithms

• Many tradition parallel algorithms require the parallel processes to synchronize at regular and frequent intervals to exchange data and continue from known points

This is bad for grid computations!!All traditional parallel algorithms books have to

be thrown away for grid computing.

Techniques to reduce actual synchronization communications

• Asynchronous algorithms – Algorithms that do not use synchronization

at all

• Partially synchronous algorithms– those that limit the synchronization, for

example only synchronize on every n iterations

– Actually such algorithms known for many years but not popularized.

Big Problems“Grand challenge” problems

Most of the high profile projects on the grid involve problems that are so big usually in number of data items that they cannot be solved otherwise

Examples

• High-energy physics

• Bioinformatics

• Medical databases

• Combinatorial chemistry

• Astrophysics

Workflow Technique

• Use functional decomposition - dividing problem into separate functions which take results from other functions units and pass on results to functional units - interconnection patterns depends upon the problem.

• Workflow - describes the flow of information between the units.

ExampleClimate Modeling

Atmospheric Atmospheric

Hydrology

Land Surface ModelOceanic Circulation

Atmospheric Model

ChemistryCirculation Model

Model

Ocean Model

Ocean Chemistry

heating rates

water vapor content, humidity , pressure,wind velocities, temperature

sea surf ace temperature

wind stress,heat flux,water flux