1. Computational Grids

2. Computational Problems
Problems that have lots of computations and usually lots of data.

3. 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.

4. 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.

5. Weather Forecasting
Atmosphere modeled by dividing it into 3-dimensional cells.
Calculations of each cell repeated many times to model passage of time.

6. 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).

7. 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.

8. 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.

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

10. 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.

11. 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.

12. Speedup Factor ts S(p) = = tp
Execution time using one processor (best sequential algorithm)
S(p) = = tp
Execution time using a multiprocessor with p processors
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.

13. 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

14. Maximum Speedup Amdahl’s lawt s ft (1 - f ) t s s
Parallelizable sections
Serial section
(a) One processor
(b) Multiple
processors
p processors (1 - f ) t / p t s p

15. Speedup factor is given by:
This equation is known as Amdahl’s law

16. Speedup against number of processors
= 0% 20 16
Speedup factor, S(p) 12 f
= 5% 8 f
= 10% 4 f
= 20% 4 8 12 16 20
Number of processors, p

17. Even with infinite number of processors, maximum speedup limited to 1/f.
Example
With only 5% of computation being serial, maximum speedup is 20, irrespective of number of processors.

18. Superlinear Speedup Example - Searching
(a) Searching each sub-space sequentially
Start
Time t s t /p s
Sub-space D t
search x t /p s
Solution found x
indeterminate

19. (b) Searching each sub-space in parallel
Solution found D t
(b) Searching each sub-space in parallel

20. What is the speed-up now?
Question
What is the speed-up now?

21. Speed-up then given by t x s + D t p
S(p) = D t

22. p – 1 ´ t + D t s p S(p) = ® ¥ D t as D t tends to zero
Worst case for sequential search when solution found in last sub-space search.
Then parallel version offers greatest benefit, i.e. p – 1 t + D t s p
S(p) = D t as D
t tends to zero   

23. 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. D t
S(p) =
= 1 D t

24. Computing Platforms for Parallel Programming

25. 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

26. Conventional Computer
Consists 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
Instructions (to processor)
Data (to or from processor)
Processor

27. 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

28. Examples
Dual Pentiums
Quad Pentiums

29. Quad Pentium Shared Memory Multiprocessor
L1 cache
L1 cache
L1 cache
L1 cache
L2 Cache
L2 Cache
L2 Cache
L2 Cache
Bus interface
Bus interface
Bus interface
Bus interface
Processor/
memory b us
I/O interf
ace
Memory controller
I/O b us
Memory
Shared memory

30. 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.

31. Parallel programming language with syntax to express parallelism
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.

32. Message-Passing Multicomputer
Complete computers connected through an interconnection network:
Interconnection
network
Messages
Processor
Local
memory
Computers

33. Dedicated cluster with a master node
External network
User
Cluster
2nd Ethernet interface
Master node
Switch
Ethernet interface
Compute nodes

34. UNC-C’s cluster used for grid course (Department of Computer Science)
coit-grid01
coit-grid02
coit-grid03
coit-grid04
3.4 GHz dual Xeon Pentiums M M M M P P P P P P P P
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.

35. 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.

36. 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.

37. 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).

38. 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

39. Multiple program, multiple data (MPMD) model
Source
Source fi le fi le
Compile to suit
processor
Executable
Processor 0
Processor p
- 1

40. Single Program Multiple Data (SPMD) model .
Different processes merged into one program. Control statements select different parts for each processor to execute.
Source fi le
Basic MPI way
Compile to suit
processor
Executables
Processor 0
Processor p - 1

41. Multiple Program Multiple Data (MPMD) Model
Separate programs for each processor. One processor executes master process. Other processes started from within master process - dynamic process creation.
Process 1
Process 2
spawn();
Time
Star
t e x
ecution
of process 2
Can be done with MPI version 2

42. 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.

43. 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();
else
slave();
MPI_Finalize(); }
where master() and slave() are to be executed by master process and slave process, respectively.

44. Basic “point-to-point” Send and Receive Routines
Passing a message between processes using send() and recv() library calls:
Process 1
Process 2
send(&x, 2);
recv(&y, 1); x y Mo v
ement
of data
Generic syntax (actual formats later)

45. 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().

46. Message Tag Example
To send a message, x, with message tag 5 from a source process, 1, to a destination process, 2, and assign to y:
Process 1
Process 2
send(&x,2, 5 );
recv(&y,1, x y Mo v
ement
of data W
aits f
or a message from process 1 with a tag of 5

47. 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.

48. Synchronous send() and recv() using 3-way protocol
Process 1
Process 2
Time
Request to send
send();
Suspend Ac
kno
wledgment
process
recv();
Both processes
Message
continue
(a) When
send()
occurs before
recv()

49. Synchronous send() and recv() using 3-way protocol
Process 1
Process 2
Time
recv();
Suspend
Request to send
send();
process
Both processes
Message
continue Ac
kno
wledgment
(b) When
recv()
occurs before
send()

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

51. 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.

52. 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.

53. How message-passing routines return before message transfer completed
Message buffer needed between source and destination to hold message:
Process 1
Process 2
Message b
uff er
Time
send();
Contin ue
recv();
Read
process
message b
uff er

54. 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.

55. 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

56. Parameters of MPI blocking receive
MPI_Recv(buf,count,datatype,dest,tag,comm,status)
Datatype of each item
Message tag
Address of receive buffer
Max. number of items to receive
Rank of source process
Communicator
Status after operation

57. 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) {
MPI_Recv(&x,1,MPI_INT,0,msgtag,MPI_COMM_WORLD,status); }

58. 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.

59. 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.

60. 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) {
MPI_Recv(&x,1,MPI_INT,0,msgtag, MPI_COMM_WORLD, status); }

61. “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.

62. Broadcast
Sending same message to a group of processes. (Sometimes “Multicast” - sending same message to defined group of processes, “Broadcast” - to all processes.)
Process 0
Process 1
Process p - 1
data
data
data
Action
buf
MPI_bcast();
MPI_bcast();
MPI_bcast();
Code
MPI form

63. MPI Broadcast routine Actions: Parameters:
int MPI_Bcast(void *buf, int count, MPI_Datatype datatype, int root, MPI_Comm comm)
Actions:
Broadcasts message from root process to al
l processes in comm and itself.
Parameters:
*buf message buffer
count number of entries in buffer
datatype data type of buffer
root rank of root

64. Scatter
Sending each element of an array in root process to a separate process. Contents of ith location of array sent to ith process.
Process 0
Process 1
Process p - 1
data
data
data
Action
buf
MPI_scatter();
MPI_scatter();
MPI_scatter();
Code
MPI form

65. Gather
Having one process collect individual values from set of processes.
Process 0
Process 1
Process p - 1
data
data
data
Action
buf
MPI_gather();
MPI_gather();
MPI_gather();
Code
MPI form

66. Reduce
Gather operation combined with specified arithmetic/logical operation.
Example: Values could be gathered and then added together by root:
Process 0
Process 1
Process p - 1
data
data
data
Action
buf +
MPI_reduce();
MPI_reduce();
MPI_reduce();
Code
MPI form

67. 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

68. Example
To 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.

69. Sample MPI program #include “mpi.h” #include <stdio.h>
#include <math.h>
#define MAXSIZE 1000
void 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();
Sample MPI program

70. Debugging/Evaluating Parallel Programs Empirically

71. Visualization Tools Programs can be watched as they are executed in a space-time diagram (or process-time diagram):
Process 1
Process 2
Process 3
Computing
Time W
aiting
Message-passing system routine
Message
Visualization tools available for MPI. An example - Upshot

72. Evaluating Programs Empirically Measuring 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).

73. 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.

74. Compiling/Executing MPI Programs Basics
For MPICH, use two commands:
mpicc to compile a program
mirun to execute program

75. 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.

76. mpirun Example mpirun –np 3 hello
executes 3 instances of hello on the local machine (when using MPICH).

77. Using multiple computers
First create a file (say called “machines”) containing list of computers you what to use.
Example
coit-1grid01.uncc.edu
coit-2grid01.uncc.edu
coit-3grid01.uncc.edu
coit-4grid01.uncc.edu

78. 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.)

79. 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.

80. Sample MPI Programs

81. Hello World Printing 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; }

82. 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?

83. Answer
Several possible outputs depending upon order processes are executed.
Example
Hello World from process 2 of 4
Hello World from process 0 of 4
Hello World form process 1 of 4
Hello World form process 3 of 4

84. 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;

85. 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

86. Easy then to add name in greeting with:
sprintf(greeting,"Hello World from process %d of %d on $s\n", rank, size, procname);

87. Pinging processes and timing Master-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;

88. Master routine void 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); }

89. Slave routine void 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); }

90. Example using collective routines MPI_Bcast() MPI_Reduce()
Adding numbers in a file.

91. #include “mpi.h”
#include <stdio.h>
#include <math.h>
#define MAXSIZE 1000
void 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();

92. 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.

93. MPI C 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)

94. Example Getting 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; }

95. Executing MPI program with command line arguments
mpirun -np 2 myProg
argv[0]
argv[2]
argv[1]
Removed by MPI - probably by
MPI_Init()
Remember these array elements hold pointers to the arguments.

96. 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:
LAM MPI:

97. Parallel Programming Home Page
Gives step-by-step instructions for compiling and executing programs, and other information.

98. Grid-enabled MPI

99. Several versions of MPI developed for a grid:
MPICH-G, MPICH-G2
PACXMPI
MPICH-G2 is based on MPICH and uses Globus.

100. MPI code for the grid No difference in code from regular MPI code.
Key aspect is MPI implementation:
Communication methods
Resource management

101. 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

102. 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.

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

104. Running an MPICH-G2 Program mpirun
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.

105. 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)

106. “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.

107. 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

108. 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.

109. Example With the machines file containing: “coit-0grid01.uncc.edu” 4
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.

110. mpirun with 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.

111. mpirun -dumprsl -np 2 myprog
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.

112. mpirun -globusrsl myRSL.rsl
Given rsl file, myRSL.rsl, use:
mpirun -globusrsl myRSL.rsl
to submit modified script.

113. 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

114. 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.

115. More information on MPICH-G2

116. Parallel Programming Techniques Suitable for a Grid

117. Message-Passing on a Grid
VERY expensive, sending data across network costs millions of cycles
Bandwidth shared with other users
Links unreliable

118. Computational Strategies
As a computing platform, a grid favors situations with absolute minimum communication between computers.

119. With no/minimum communication:
Strategies
With 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

120. 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).
No communication or very little communication between processes.
Each process can do its tasks without any interaction with other processes

121. Monte Carlo Methods An embarrassingly parallel computation.
Monte Carlo methods use of random selections.

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

123. Ratio of area of circle to square given by
Area of square x
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.

124. Method actually computes an integral.
One quadrant of the construction can be described by integral

125. So can use method to compute any integral
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).

126. 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. X1 X2
Area
f(x) x d 1 2 ò N -
lim
f( xr) r i = å
(x2 – x1)

127. Example ò 2 Sequential Code x 1 Computing the integral (x2 – 3x) dx
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. x 1 2 ò
(x2 – 3x) dx

128. 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.

129. 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.

130. Techniques to reduce effects of network communication
Latency hiding with communication/computation overlap
Better to have fewer larger messages than many smaller ones

131. 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.

132. 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.

133. 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

134. Examples High-energy physics Bioinformatics Medical databases
Combinatorial chemistry
Astrophysics

135. 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.

136. Example Climate Modeling