CPSC457 Assignment 3-Multithreading-Prime-Number-Detector Solved

Q1. Programming question – calculating 𝛑
Improve the performance of an existing single-threaded calcpi program by converting it to a

multi-threaded implementation. Download the starter code, compile it, and run it:

The calcpi program estimates the value of π using an algorithm described in https://en.wikipedia.org/wiki/Approximations_of_%CF%80#Summing_a_circle’s_area, and it is implemented inside the function count_pi() in file calcpi.cpp.

The included driver (main.cpp) parses the command line arguments, calls count_pi() and prints the results. The driver takes 2 command line arguments: an integer radius and number of threads. For example, to estimate the value of π using radius of 10 and 2 threads, you would run it like this:

The function uint64_t count_pi(int r, int N) takes two parameters – the radius and number of threads, and returns the number of pixels inside the circle or radius 𝑟 centered at (0,0) for every pixel (𝑥, 𝑦) in squre −𝑟 ≤ 𝑥, 𝑦 ≤ 𝑟. The current implementation is single threaded, so it ignores the N argument. Your job is to re-implement the function so that it uses N threads to speed up its execution, such that it runs N times faster with N threads on hardware where N threads can run concurrently. Please note that your assignment will be marked both for correctness and the speedup it achieves.

You need to find a way to parallelize the algorithm without using any synchronization mechanisms, such as mutexes, semaphores, atomic types, etc. You are only allowed to create and join threads.

Write all code into calcpi.cpp and submit this file for grading. Make sure your calcpi.cpp works with the included driver program. Your TAs may use a different driver program during

Q3. Programming question – detecting primes [30 marks]

Convert a single-threaded program detectPrimes to a multi-threaded implementation. Start by downloading the single-threaded code, then compile it and run it:

The detectPrimes program reads integers in range [2, 263 − 2] from standard input, and then prints out the ones that are prime numbers. The first invocation example above detects prime numbers 3, 19 and 1033 in a file example.txt. The second invocation uses the program to find all primes in the range [1017, 1017 + 300]. If duplicate primes appear in the input, they will be duplicated in the output.

detectPrimes accepts a single command line argument – a number of threads. This parameter is ignored in the current implementation because it is single threaded. Your job is to improve the execution time of detectPrimes by making it multi-threaded, and your implementation should use the number of threads given on the command line. To do this, you will need to re-implement the function:

which is defined in detectPrimes.cpp. The function takes two parameters: the list of numbers to test, and the number of threads to use. The function is called by the driver (main.cpp) after parsing the standard input and command line. Your implementation should use n_threads number of threads. Ideally, if the original single-threaded program takes time 𝑇 to complete a test, then your multi-threaded implementation should finish that same test in 𝑇/𝑁 time when using 𝑁 threads. For example, if it takes 10 seconds to complete a test for the original single- threaded program, then it should take your multi-threaded program only 2.5 seconds to complete that same test with 4 threads. To achieve this goal, you will need to design your program so that:

• You give each thread the same amount of work;
CPSC 457: Assignment 3 3

std::vector<int64_t>
detect_primes(const std::vector<int64_t> & nums, int n_threads);

• your multi-threaded implementation does the same amount of work as the single-threaded version; and
• the synchronization mechanisms you utilize are efficient.

  Your TAs will mark your assignment by running the code against multiple different inputs and using different numbers of threads. To get full marks for this assignment, your program needs to output correct results but also achieve near optimal speedup for the given number of threads and available cores. If your code does not achieve optimal speedup on all inputs, you will lose some marks for those tests.

  You may assume that there will be no more than 100,000 numbers in the input, and that all numbers will be in the range [2, 263 − 2]. Some inputs will include many numbers, some inputs will include just few numbers, some numbers will be large, some small, some will be prime numbers, others will be large composite numbers, etc… For some numbers it will take long time to compute their smallest factor, for others it will take very little time. You need to take all these possibilities into consideration. Design your own test inputs and test your code thoroughly.

  Write all code into detectPrimes.cpp and submit it for grading. Make sure your detectPrimes.cpp works with the included main.cpp driver. We may use a different driver during marking, so it is important that your code follows the correct API. Make sure your program runs on linuxlab.cpsc.ucalgary.ca.

  You may use any of the synchronization mechanisms we covered in lectures, such as semaphores, mutexes, condition variables, spinlocks, atomic variables, and barriers. Don’t forget to make sure your code compiles and runs on linuxlab.cpsc.ucalgary.ca.

  Please note that the purpose of this question is NOT to find a more efficient factorization algorithm. You must implement the exact same factorization algorithm as given in the skeleton code, except you need to make it multi-threaded.

  Q4 – Written question (5 marks)

  Time the original single-threaded detectPrimes.cpp as well as your multi-threaded version on three files: medium.txt, hard.txt and hard2.txt. For each of these files, you will run your solution 6 times, using 1, 2, 3, 4, 8 and 16 threads. You will record your results in 3 tables, one for each file, formatted like this:

# threads

original program 1
2
3
4
8
16

Observed timing

medium.txt

Observed speedup compared to original

1.0

Expected speedup

1.0 1.0 2.0 3.0 4.0 8.0 16.0

CPSC 457: Assignment 3

4

The ‘Observed timing’ column will contain the raw timing results of your runs. The ‘Observed speedup’ column will be calculated as a ratio of your raw timing with respect to the timing of the original single-threaded program. Once you have created the tables, explain the results you obtained. Are the timings what you expected them to be? If not, explain why they differ.

Submission

Submit the following files to D2L for this assignment.

Do not submit a ZIP file. Submit individual files.

calcpi.cpp detectPrimes.cpp report.pdf

solution to Q1
solution to Q3
answers to all written questions

Please note – you need to submit all files every time you make a submission, as the previous submission will be overwritten.

 

Hint 3 –good solution

Even more efficient approach would be to parallelize the inner loop (the loop inside the is_prime function). In this approach, all threads would test the same number for primality. If you choose this approach, you need to give each thread a different portion of divisors to check. This will allow you to handle more input cases than the simple solution mentioned earlier. For extra efficiency, and better marks, you also need to consider implementing thread re-use, e.g., by using barriers. Here is a possible rough outline of an algorithm that you could implement:

detectPrimes():
prepare memory for each thread
initialize empty array result[] – this could be a global variable set global_finished = false – make it atomic to be safe
start N threads, each runs thread_function() on its own memory join N threads
return results

thread_function():
  repeat forever:

    serial task – pick one thread using barrier
      get the next number from nums[]
      if no more numbers left:

        set global_finished=true to indicate to all threads to quit
      otherwise:

        divide work for each thread
    parallel task – executed by all threads, via barrier

      if global_finished flag is set, exit thread

      otherwise do the work assigned above and record per-thread result
    serial task – pick one thread using barrier

      combine the per-thread results and update the result[] array if necessary

You may use my C++ barrier implementation from lecture notes.

Hint 4 – best solution

This builds on top of the hint 3 above, but it also adds thread cancellation. You need cancellation for cases where one of the threads discovers the number being tested is not a prime, so that it can cancel the work of the other threads. Thread cancellation sounds simple to implement, but it does take non-trivial effort to get it working correctly.

Appendix – Approximate grading scheme for Q3

The test cases that we will use for marking will be designed so that you will get full marks only if you implement the most optimal solution. However, you will receive partial marks even if you one of the less optimal solutions. Here is the rough breakdown of what to expect depending on which solution you implement:

• Parallelization of outer loop with fixed amount of work will yield ~9/28 marks
• Parallelization of outer loop with dynamic work will yield ~15/28 marks
• Parallelization of inner loop without work cancellation and without thread reuse will yield

  ~19/28 marks

• Parallelization of inner loop with thread reuse but without cancellation will yield ~24/28 marks.
• Parallelization of inner loop with thread reuse and with cancellation will give 28/28 marks.

  Any tests on which your program produces wrong results will receive 0 marks.