The merge sort

The algorithm you have to parallelize is the merge sort. The reason the merge sort was chosen is that it is almost the perfect algorithm to parallelize. Just to remind you, the merge sort breaks the data to be sorted into two halves, sorts the halves recursively and merges the two sorted halves back together to give the answer.

The version of the merge sort you have to use is written in C and available on the assignment Canvas page as a1.0.c.

In all of the work which follows do NOT optimize the C compilations. Always compile using:

filename.c -o filename (you will need to use -pthread for some programs).

Do all of the timings on the same (or very similar) machine and don’t watch videos or do similar things while you are taking the timings. Take the timings at least 3 times and average them.

Things to do

Step 0

Read through and understand the code in the file a1.0.c.

Compile and run the program. An important part of the program is the is sorted function before the end. You will always need to call this to ensure that any changes you make to the implementation do in fact return the sorted data.

If you run the program without any command line parameters e.g./a1.0

it will use a default array of only two values.

Run it with a larger amount of random data by including the size parameter on the command line e.g../a1.0 1000

runs the program with an array of 1000 random values.

Determine how large an array can be dealt with by this program before you get a segmentation fault.

Segmentation faults happen when something goes wrong with memory accesses or allocations(a segment is an area of memory). In our case the program allocatesspace for the array of values, and extra working space, on the stack, and as the size of the array increases eventually we run out of stack space.

Question 1: What environment did you run the assignment on (e.g., operating system, number of cores, amount of real memory)?

Hint: man uname, man free and man lscpu.

The output of uname -a provides some of this information, free provides information on the amount of memory, and lscpu provides information on the number of CPUs. Also mention whether you were using a virtual machine and if so say which one.

What approximate size for the array can you get to in the original program before a segmentation error occurs?

Step 1

Modify the program (call it a1.1.c) to increase the amount of stack space so that the program can at least deal with 100,000,000 numbers. Hint: man getrlimit and setrlimit.

Time how long it takes the program to sort 100,000,000 numbers and record the result.

Question 2 : Explain why the limit on the stack size is considerably smaller than the amount of memory available to other sections of memory which are marked as “unlimited”?

Step 2

Modify the program (call it a1.2.c) to use two threadsto perform the sort.

You will need to make sure you are running on a machine with at least 2 cores. If you are using a virtual machine you may need to change the configuration to use at least 2 cores.

The FlexIT Ubuntu image has at least 4 cores.

Hint: man pthread_create, pthread_join

Each pthread has its own stack and the standard pthread stack size is very limited (why do you think this is so?). So you will need to increase the stack size. You need to change the pthread attributes to do this.

Hint: man pthread_attr_init, pthread_attr_setstacksize

Time how long it takes the program to sort 100,000,000 numbers and record the result.

Question 3 : Explain how you parallelized the sort and compare the times you observe with the times from Step 1. Explain why the times are different.

Step 3

Modify the program (call it a1.3.c) to use as many threads as there are cores to perform the sort, and no more.

You will need to make sure you are running on a machine with at least 4 cores. If you are using a virtual machine you may need to change the configuration to use at least 4 cores (if your computer can do this).The FlexIT Ubuntu image has at least 4 cores.

First you need a way to determine from within the program how many cores you have in the environment you are using.
Hint: man sysconf or man get_nprocs_conf

You don’t have to worry about the other work going on in the computer just proceed as if all cores are available for your sorting program.

For this step you MUST use some shared state to keep track of how many threads are currently active.Every time a new thread is started you should add one to a counter and every time a thread stops running you should reduce that counter.

Whenever you are about to call merge_sort you either start a new thread (if you haven’t reached the maximum number of cores yet) or use an ordinary function call to merge_sort from within the current thread).

The problem with this approach is that multiple threads can be accessing the shared state at the same time, so you will need to provide mutual exclusion over the thread counter.

Hint: man pthread_mutex_init, pthread_mutex_lock, pthread_mutex_unlock.

Time how long it takesthe program to sort 100,000,000 numbers and record the result. You

Step 4

Go back to step 2 and modify the program (call it a1.4.c) to use two processes rather than two threads.

Processes normally don’t share memory with each other and so there will have to be some communication between the processes. Hint: man fork, pipe.

One of the interesting thingsis that the fork system call copies the data in the parent process so that the child can see the data from the parent (at the time of the fork). This means the child process does not need to copy data from the parent to the child. However, after the child has sorted the data the resulting sorted values have to be sent back to the parent in order for it to do the merge.

Time how long it takes the program to sort 100,000,000 numbers and record the result.

Submit this program as a1.4.c

Question 5: Explain how you set up the pipes and send the sorted data back to the parent. In your answer include how the parent process knows when a child process has completed its sorting, and how it puts the received sorted data into the correct place in the main array.

Question 6: Compare the times and memory usage of this program with the earlier steps. Explain the results.

Step 5

Same as step 4 but rather than passing information back to the parent process we share the memory to be sorted in the processes. Hint: man mmap, wait.

Time how long it takes the program to sort 100,000,000 numbers and record the result. You should also take a screen shot of the System Monitor program showing the Resources tab as your program runs.

Question 7: Explain how the parent process sets up the shared memory for the child processes. In particular say whether or not the parent is sharing the same data with all the children, and why you did it that way.

Question 8 : Explain how the parent process knows when a child process has completed it sorting.

Question 9: Compare the times and memory usage of this program with the earlier steps. Explain the results.

Question 10 : Which of the steps do you consider gives the best solution? You may order the techniques from slowest to fastest and include a brief explanation of what is happening in each of them and how that relates to their performance. You may include relevant timing information and screen shots from the System Monitor.