Starting with the program provided, use the sthread_regular_for_loop() function to develop a correct and efficient multithreaded matrix multiplication function. The program consists of three files: matrix_multiply.h, matrix_multiply.c, and main.c. Write the multithreaded matrix multiplication function in matrix_multiply.c. Use the main program provided to test and time your multithreaded matrix multiplication function.

1. Hand in your modified matrix_multiply.c file.
2. Time sequential and multithreaded matrix multiply of 700-by-700 element matrices using 1, 2, 4, 8, 16, 32, 64, 96, and 128 threads on 4 processors. Hand in a table giving the execution time and speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of threads. Hand in a graph showing speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of threads.
3. Using the best number of threads from part 2, time multithreaded matrix multiply of 700-by-700 element matrices on 1, 2, 3, and 4 processors. Hand in a table giving the execution time and the speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of processors. Hand in a graph showing speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of processors.
4. Using the best number of threads from part 2, time sequential and multithreaded matrix multiply of 500-by-500, 600-by-600, 700-by-700, 800-by-800, and 900-by-900 element matrices on 4 processors. Hand in a table giving the execution time and the speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of items. Hand in a graph showing speedup of multithreaded matrix multiply over sequential matrix multiply for increasing number of items.
5. Hand in a short written performance analysis, discussing the issues that limit the speedup of multithreaded matrix multiply. Quantitatively estimate the overheads of thread management, load imbalance, and memory contention.

• Perform all timing experiments on a quad-processor Pentium Pro. For each experiment, perform 5 timing trials and report the average of the median 3 trials.
• Make sure that the machine is otherwise completely unloaded while you are performing timing experiments. Don’t touch the mouse or keyboard.
• Perform all timing experiments on programs compiled and linked using the standard Visual C++ 5.0 Release settings. Do not use additional compiler optimizations.
• For each experiment, use the value 123 as the seed for random generation of data.
• Make sure that you completely and precisely title and label tables and graphs. For example: (i) tables and graphs must have a descriptive title, (ii) columns and rows of a table must be labeled, (iii) axes of a graph must be labeled, and (iv) units must be given.
• It is an honor code violation to claim execution times that were not achieved. Claimed times must be repeatable.