Programming Assignment ZERO: Warming Up

Parallel Programming by Prof. Yi-Ping You

The purpose of this assignment is to assess whether you are familiar with Makefile and C/C++ programming. This is a calibration homework based on prerequisite material. You will receive no credit score from this assignment, but we highly encourage you to finish it. A later assignment will build upon this assignment.

Programming Assignment ZERO: Warming Up

Problem Statement

Suppose we toss darts randomly at a square dartboard, whose bullseye is at the origin, and whose sides are two feet in length. Suppose also that there is a circle inscribed in the square dartboard. The radius of the circle is one foot, and its area is π square feet. If the points that are hit by the darts are uniformly distributed (and we always hit the square), then the number of darts that hit inside the circle should approximately satisfy the equation:

Number_in_Circle/Total_Number_of_Tosses = PI/4,

since the ratio of the area of the circle to the area of the square is PI/4 (π / 4).

We can use this pseudo code to estimate the value of π with a random number generator:

number_in_circle = 0;
for ( toss = 0; toss < number_of_tosses; toss ++) {
    x = random double between -1 and 1;
    y = random double between -1 and 1;
    distance_squared = x * x + y * y;
    if ( distance_squared <= 1)
        number_in_circle++;
}
pi_estimate = 4 * number_in_circle /(( double ) number_of_tosses);

This is called a “Monte Carlo method”, since it uses randomness (the dart tosses). Write a serial C/C++ program that uses the Monte Carlo method to estimate π , with a reasonable number of tosses. You may want to use the type of long long int for the number of hits in the circle and the number of tosses, since both may have to be very large to get a reasonable estimate of π.

Hint: You may want to check if RAND_MAX is large enough for use with rand() to get a higher precision, and if the number of tosses is great enough to reach a higher accuracy.

Requirement

Your solution includes two files: a Makefile and a pi.c (in C) or a pi.cpp (in C++).
Your executable program should be named pi.out and built with the make command.
Your executable program should print out the estimated π value, which is accurate to two decimal places (i.e., 3.14xx), without any input.

You are supposed to build and run your program by simply typing make and ./pi.out. An example shows as follows.

$ make
$ ./pi.out
3.1415926....

Grading Policy

This assignment is for practice only, and you will receive no credit score from this assignment. However, some parts of the coming assignments will be based on this assignment. You should still make sure the two commands, make && ./pi.out, work as they should be.

Performance Profiling

In the future assignments, you will need to parallelize serial versions of applications. In order to identify the “hot code” of a program so as to make an effective improvement, you may need to use profiling tools to find out the program’s bottleneck. Profiling tools, such as time, gprof, and perf, provide you some useful information (e.g., call graphs, execution times, hardware events like cache-miss or branch-miss counts).

Here we give you a brief introduction on how to use these tools. For more details, please refer to the references.

`time`

The time utility executes and times the specified program command with the given arguments. It prints the elapsed time during the execution of a command, time in the system, and execution time of the time command in seconds to standard error.

For example,

time ./pi.out

`gprof`

gprof produces an execution profile of C, Pascal, or Fortran77 programs. The effect of called routines is incorporated in the profile of each caller. The profile data is taken from the call graph profile file (gmon.out default) which is created by programs that are compiled with the -pg option

Compile the program with the -pg option to instrument the program with code that enables profiling.

gcc -pg pi.c -o pi.out

Now, just execute the executable file to generate gmon.out.

./pi.out

After gmon.out is generated, the gprof tool is run with the executable name and the above generated gmon.out as arguments. The -b option suppresses the printing of a description of each field in the profile. You may also redirect stdout to a file (say, profiling_result) for later use.

gprof ./pi.out gmon.out -b > profiling_result

Read the profiling_result file to get the profiling information.

Note: If the execution time is less than 0.01 seconds, no time will be counted.

`perf`

The perf command is used as a primary interface to the Linux kernel performance monitoring capabilities and can record CPU performance counters and trace points. Similar to gprof, before you profile the program, you need to compile the program with -g option to enable profiling.

gcc -g pi.c -o pi.out

Use the perf list command to list available events.

Let’s say if we are interested in the cpu-cycles event, then we just run the program using the perf tool with the event(s) we want to monitor.

perf record -e cpu-cycles  ./pi.out

Now you can read the profiling result by running

perf report

Programming Assignment ZERO: Warming Up

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