Lab 9: Thread Level Parallelism

Deadline: Monday, November 14, 11:59:59 PM PT

Lab Section Slides

Setup

Warning: We strongly recommend working on the hive machines for this lab. OpenMP may perform differently on your local machine, and installing it can be annoying.

In your labs directory, pull the files for this lab with:

git pull starter main

Info: OpenMP

OpenMP stands for Open specification for Multi-Processing. It is a framework that offers a C interface. It is not a built-in part of the C language -- most OpenMP features are compiler directives. (One example of a compiler directive you've seen in the past is #include.)

Benefits of multi-threaded programming using OpenMP include:

  • A very simple interface that allows a programmer to separate a program into serial regions and parallel regions.
  • Convenient synchronization control (data race bugs in threads are very hard to trace).

In this lab, we'll practice some basic usage of OpenMP. OpenMP is already installed on hive machines, so we strongly recommend that you work on the hive machines for this lab.

Exercise 1: OpenMP Hello World

Consider the sample hello world program (hello.c), which prints "hello world from thread #" from each thread:

int main() {
    #pragma omp parallel
    {
        int thread_id = omp_get_thread_num();
        printf("hello world from thread %d\n", thread_id);
    }
}

This program will create a team of parallel threads. Each thread prints out a hello world message, along with its own thread number.

Let's break down the #pragma omp parallel line:

  • #pragma tells the compiler that the rest of the line is a directive.
  • omp declares that the directive is for OpenMP.
  • parallel says that the following block statement -- the part inside the curly braces ({/}) -- should be executed in parallel by different threads.

IMPORTANT When writing your own code, ensure that you place the opening curly brace on a new line. Do not put it on the same line as the directive.

You can change the number of OpenMP threads by setting the environment variable OMP_NUM_THREADS or by using the omp_set_num_threads function before the parallel section in your program.

Try running the program:

make hello
./hello

If you run ./hello a couple of times, you may notice that the printed numbers are not always in increasing order and will most likely vary across runs. This is because we didn't specify any sort of synchronization options, so OpenMP will not enforce any execution order. (More on that later.) It is also important to note that the variable thread_id is defined inside the parallel block, which means that each thread has its own copy of thread_id. In general with OpenMP, variables declared inside the parallel block will be private to each thread, but variables declared outside a parallel block will be shared across all threads. There are ways to override this, but more on that later.

Exercise 2: Vector Addition

Vector addition is a naturally parallel computation, since it's an elementwise operation (element i of the result vector does not depend on elements j != i), so it makes for a good first exercise. The v_add() functions inside omp_apps.c will store the sum of input vectors x and y into the result vector z. A first attempt at this might look like:

void v_add(double* x, double* y, double* z) {
    #pragma omp parallel
    {
        for(int i=0; i<ARRAY_SIZE; i++)
        {
            z[i] = x[i] + y[i];
        }
    }
}

Try running the tests:

make v_add
./v_add

The testing framework will time the function execution for different thread counts. You should observe that this implementation performs worse as we increase the number of threads! Why?

The issue is that each thread is executing all of the code within the omp parallel block. If we have 8 threads, we'll actually be performing the same vector addition 8 times! Not only that, but various threads writing to the same variables in memory may cause a decrease in performance due to cache synchronization. Rather than have each thread run every iteration of the for loop, we need to split the for loop iterations across all the threads so each thread does only a portion of the work.

OpenMP has built-in functionality for dividing up the work of for loops among threads. To tell openMP to split up the work among multiple threads, you would use #pragma omp parallel for as seen below:

void v_add(double* x, double* y, double* z) {
    #pragma omp parallel for
    for(int i=0; i<ARRAY_SIZE; i++)
    {
        z[i] = x[i] + y[i];
    }
}

Note that there are no opening and closing brackets around the parallel section. The #pragma omp parallel for directive can only be placed directly before a for loop.

Action Items

For this exercise, we'd like you to try to understand what is happening under the hood of this operation by manually splitting the for loop iterations among threads. Your task is to optimize v_add(). Your implementations should use the following 2 functions -- don't hardcode thread counts or thread IDs:

  • int omp_get_num_threads() - returns the current total number of OpenMP threads. Note that the number of threads will be 1 outside of an OpenMP parallel section.
  • int omp_get_thread_num() - returns the thread number of the current thread, commonly used as thread ID.

There are two ways that you can split up work:

Slices

Start with implementing v_add_optimized_adjacent() (found in omp_apps.c), which separates the vectors into element-wise slices.

Chunks

Then, implement v_add_optimized_chunks() which separates the vectors into contiguous chunks. As an example, if we have 3 threads, thread 0 will handle the first third of the elements in the array, thread 1 will handle the second third, and thread 3 will handle the last third. Remember to handle the "tail case" -- depending on your chunking logic, the last chunk may have slightly more or less elements than the others.

For this exercise, you CANNOT use #pragma omp parallel for. You must manually split up the work of the threads.

Remember that speedup may increase slower after a certain number of threads, since part of the whole program is not parallelizable.

Question

Which version of your code runs faster, chunks or adjacent? Why? Chunks performs better than adjacent because adjacent indexing is more susceptible to false sharing: when different threads write to different elements in the same cache block in their own cache.

Exercise 3: Dot Product

The next task is to compute the dot product of two vectors. At first glance, implementing this might seem not too different from v_add, since we should now just perform elementwise multiplication instead of addition. The challenge is how to add the products into one variable (aka reduction) to get our final answer. If multiple threads try to add their results to the same variable at the same time, it will lead to a data race which will result in an incorrect result.

One solution is to use a critical section. The code in a critical section can only be executed by a single thread at any given time. Thus, having a critical section naturally prevents multiple threads from reading and writing to the same data, a problem that would otherwise lead to data races. OpenMP provides the critical primitive to allow you to perform computations within a critical section. An implementation, dotp_naive() in omp_apps.c, protects the sum with a critical section.

double dotp_naive(double* x, double* y, int arr_size) {
    double global_sum = 0.0;
    #pragma omp parallel
    {
        #pragma omp for
        for (int i = 0; i < arr_size; i++)
            #pragma omp critical
            global_sum += x[i] * y[i];
    }
    return global_sum;
}

Try running the tests:

make dotp
./dotp

Notice how the performance gets much worse as the number of threads go up? By putting all of the work of reduction in a critical section, we have flattened the parallelism and made it so only one thread can do useful work at a time (not exactly the idea behind thread-level parallelism). This contention is problematic; each thread is constantly fighting for the critical section and only one is making any progress at any given time. As the number of threads go up, so does the contention, and the performance pays the price. Can we reduce the number of times that each thread needs to use a critical section?

OpenMP has a built in way to reduce this problem through the use of the reduction keyword. The reduction keyword will increase the parallelizability of your code by automatically reducing the amount of code contained within the critical section. To use this keyword, you must specify the the variable that should be in a critical section and the operation being performed on that variable. Here is the code with the reduction keyword:

double dotp_reduction_optimized(double* x, double* y, int arr_size) {
   double global_sum = 0.0;
   #pragma omp parallel
   {
       #pragma omp for reduction(+:global_sum)
       for (int i = 0; i < arr_size; i++) {
           global_sum += x[i] * y[i];
       }
   }
   return global_sum;
}

Here, the variable that should only be accessed by one thread at a time is global_sum and the operation being performed on it is addtion (+).

Action Items

We'd like you to understand what is going on under the hood of this operation. Let's improve the performance of the program without using the reduction keyword. Write your implementation in dotp_manual_optimized(). Remember that we want to reduce the number of times each thread enters the critical section.

Hint Each thread should have it's own local sum. Once each thread is finished computing its local sum, you can add all of the sums together in a critical section.

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Submission

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