Parallel Computing Lab Solution

$30.00

Description

Introduction

Most of what youve learned so far in CS 2400 and CS2401 involves programs that execute sequentially. These programs execute a first step, then a second step, etc. In this lab, we will provide an introduction to programs that can execute more than one instruction at the same time. These programs will be called parallel programs, and, in theory, they should be able to run much faster than their sequential counterparts.

Parallel processing is becoming increasingly important in our modern society. Many

modern devices (cellphones, computers) have multiple processors (or cores). Likewise, many industrial scale computing applications (e.g., Google search), use scores of computing devices in modern datacenters. The machines that you are using also have multiple processing units (cores) within a single physical processor.

Investigating Your Lab Machine

The Solaris version of UNIX provides a command (psrinfo) that provides information about the number processors (both the number of physical processors as well as the number of cores). Issue the command

man psrinfo

to see how to use the psrinfo command.

In order to see the number of physical processors on your lab machine, issue the command

/usr/sbin/psrinfo p

1. (10 pts.) How many physical processors are on the lab machines that you are currently working on?

Now, enter the command

/usr/sbin/psrinfo v

2. (10 pts.) How many virtual processors are there on your lab machine?

3. (10 pts.) How fast (in terms of GHz) is each virtual processor on your lab machine? While the psrinfo command provides a lot of information, it cannot distinquish between

a processing core and a hyperthreaded virtual processor. To get that information, youll need to use the kstat command.

Issue the command

kstat | grep core

and examine the output to determine how many physical cores are on your lab machine.

4. (10 pts.) How many cores are on your physical lab machine?

Exploiting Multiple Processors in C++: MultiThreaded

Applications

Next, we will see how to use these multiple CPU cores in your C++ programs to make then run faster.

First, we must discuss a little bit about how to use all of the physical cores on a machine

in a single program. The way to do this is to use either multiple processes or multiple threads. A process is a running program. Two processes do not share the same address space. A thread is a lightweight process, and can share the same address space.

Next, we must discuss how to create a C++ program that uses multiple threads. The easiest way to do this is to use the OpenMP standard. The OpenMP standard provides a set of compiler directives that can be used to seamlessly create programs that execute with multiple threads. OpenMP hides many of the implementation details, and so it is easy to make mistakes. However, once you have a basic understanding of how OpenMP works, it can be very easy to write programs that use multiple threads.

The simplest compiler directive provided by OpenMP is the compiler directive

#pragma omp parallel for

If you add this compiler directive, and if you compile your code with the flag -fopenmp, then your program may run faster. (Remember, if you forget the flag -fopenmp, this compiler directive will be ignored.)

This compiler directive tells the compiler to break the following for loop into n equal size chunks,” where n is the number of processors on the machine, and to execute n separate for loops (in separate threads) to execute the forloop. Now, notice, that not every for loop can be executed in this way, since (i) sometimes, one iteration of the forloop may depend on previous iterations of the forloop, and (ii) sometimes, a shared variable may appear in the forloop. If a shared variable appears in the forloop, and it is modified, then executing that loop using multiple threads may generate the wrong answer. Hence, the code that modifies that shared variable becomes a critical section, i.e., a section of code that can be executed by only one thread at a time. In OpenMP, you can denote a critical section using the compiler directive:

#pragma omp critical

Lets look at an example of how to use #pragma omp parallel for. can be used.

Matrix Multiplication

A matrix is simply a two-dimensional array of numbers. A single n × n matrix A has n rows and n columns. Each individual element of A is identified by its location. So, the element Ai,j is located in row i and column j. If we have two n × n matrices A and B, we can multiply these two matrices to compute a third matrix C . In particular, C is defined as

follows:

n

Ci,j = X Ai,k Bk,j (1)

l=1

A straightforward implementation of matrix multiplication can be found in labp1.cc. An input to this program is given in the file 900.dat.

5. (10 pts.) Compile labp1.cc and run it on the input 900.dat. What is the output?

6. (10 pts.) Run your program again. This time, use the UNIX time command to see how long it takes. How long did it take to run?

Insert the line

#pragma omp parallel for

at line 13 in the program labp1.cc.

7. (10 pts.) Compile your modified program using the appropriate compiler flag. Run this new program on 900.dat? What was the output?

8. (10 pts.) Run your program again. This time, use the UNIX time command to see how long it takes. How long did it take to run?

Efficiency and Speedup

If you successfully completed the previous problems, you should have noticed that second program was much faster. The ratio of the time taken by the first program (the sequential version) and the time taken by the second program (the parallel version) is called speedup. Ideally, the speedup that a parallel program achieves over the sequential version should be near to the number of processors utilized. The efficiency achieved by a parallel program is the speedup divided by the number of processors. So, for example, if a sequential program takes 10 seconds to execute and the parallel version takes 2 seconds, then the speedup is 5. If the number of processors used is 8, the efficiency is 5/8 = 62.5 %.

9. (5 pts.) What speedup did you achieve on the parallel version of labp1.cc?

10. (5 pts.) What efficiency did you achive on the parallel version of labp1.cc?

Putting it all together

Consider the program labp2.cc and the input 900_2.dat.

11. (10 pts.) Add OpenMP compiler directives to labp2.cc so that it executes in parallel and computes the same value as the original code. (Hint, you may need to define a critical section. Also, do not try to speed up reading in the input.) Check with your lab TA to see that youve done it correctly.

Does your code run faster than the original?