In this project, I wrote two independent programs, thr_atomic.c and thr_reduce.c, each of which uses m computational threads to concurrently calculate the sum of square roots from 1 to n, where m and n are powers of 2 and are specified in the command line.

For the program thr atomic.c, it gets the values m and n from the command line arguments and converts them to two integers, respectively. Next, it creates m threads using pthread_create() and each thread computes the sum of n/m square roots. Namely, the first thread (i.e. thread 0) computes the sum of square roots from 1 to n/m, the second thread (i.e. thread 1) computes the sum of the square roots from n/m+1 to 2n/m, etc. When a thread finishes its computation, it should print its partial sum and atomically add it to a shared global variable. Our program then lets the main thread know that all of the m computational threads have done the atomic additions and hence it can print the result. Below is an example of running tbis thread program:

bach> ./thr_atomic 2 65536

thr 0: 3954518.036356

thr 1: 7230420.422587

sum of square roots: 11184938.458943

The program thr_reduce.c is similar to thr_atomic.c except that we need to use the parallel reduction approach to combine the partial sums. That is, our program uses a shared global array and each computational thread stores its partial sum, but not prints, in an array element indexed on its thread ID. Then, half of these threads call pthread_join() to wait for their corresponding partner threads completion, and then each of these threads can add two numbers in the array together. This reduction procedure will be performed log(m) times and each time the number of the active threads will be reduced half. Finally, there will be only one active thread and this thread should print the whole array.

For example, assume that there are 8 computational threads. In the first reduction step (i.e. adding two partial sums in the array), thread 0 should wait for thread 4 done, thread 1 has to wait for thread 5 done, threads 2 needs to wait for thread 6 done, and thread 3 should wait for thread 7 done. In the second reduction step, thread 0 waits for thread 2 finished, and thread 1 waits for thread 3 finished. In the third step, thread 0 waits for thread 1 done and then prints the the whole array. Hint: to find its partner thread ID during the ith reduction step, a thread can use its ID XORed with 2r−i , where r = log(m). Note that the main thread needs to use a reverse loop to create threads. That is, the thread with the highest ID (m-1) will be created first and the thread with ID 0 last. The main thread just calls pthread_exit() after creating m threads. It does not need to wait for these threads. Calling pthread_exit() in the main thread will allow other threads to continue execution.

After both programs were completed, we have created a makefile, that calls and executes all of the functions within thr_atomic.c and thr_reduce.c and makes both of those programs executable.