General Performance Considerations
Sources of Overhead
Overheads are the costs associated with managing parallelism that can impact overall performance. The main sources of overhead include:
Communication Overhead
- Data Transfer: When using multiple threads or processes, data often needs to be transferred between computational units. Inter-process communication (IPC) or data exchange between threads can be costly, especially with large volumes of data.
- Synchronization: Synchronization mechanisms (such as semaphores, locks, or barriers) introduce overhead. Excessive synchronization can lead to significant slowdowns.
Example:
#pragma omp parallel
{
#pragma omp critical
{
// Critical section where threads synchronize
}
}
Thread Management Overhead
- Thread Creation and Destruction: Frequently creating and destroying threads can incur overhead. It’s often more efficient to reuse threads when possible.
Example: Using thread pools to avoid frequent creation and destruction of threads.
Synchronization Overhead
- Concurrent Access: Managing concurrent access to shared resources (like global variables) requires synchronization mechanisms, which can introduce substantial overhead.
Example:
#include <omp.h>
int main() {
int sum = 0;
#pragma omp parallel
{
#pragma omp for
for (int i = 0; i < 100; i++) {
#pragma omp critical
sum += i;
}
}
printf("Sum is %d\n", sum);
}
- Embarrassingly Parallel Applications and Those That Aren’t
Embarrassingly Parallel Applications
Embarrassingly parallel applications are those that can be easily parallelized with little to no need for communication or synchronization between tasks. These are ideal for parallel computing as they maximize resource utilization with minimal overhead.
Examples:
- Image processing where each pixel can be processed independently.
- Monte Carlo simulations where each simulation is independent.
Code Example:
#include <omp.h>
#include <stdio.h>
int main() {
int N = 100000;
int* array = (int*)malloc(N * sizeof(int));
#pragma omp parallel for
for (int i = 0; i < N; i++) {
array[i] = i * 2;
}
free(array);
return 0;
}
Non-Embarrassingly Parallel Applications
Non-embarrassingly parallel applications often require synchronization or communication between tasks. This can include algorithms that require shared information or coordination between tasks.
Examples:
- Sorting algorithms that require data sharing between different phases.
- Numerical computations with dependencies between tasks.
Code Example:
#include <omp.h>
#include <stdio.h>
int main() {
int N = 100;
int* array = (int*)malloc(N * sizeof(int));
int* results = (int*)malloc(N * sizeof(int));
// Initialize array
for (int i = 0; i < N; i++) {
array[i] = i;
}
#pragma omp parallel
{
int tid = omp_get_thread_num();
#pragma omp for
for (int i = 0; i < N; i++) {
results[i] = array[i] * array[i];
}
}
free(array);
free(results);
return 0;
}
Task Assignment: Static vs. Dynamic
Static Task Assignment
Static task assignment divides the work into fixed chunks and assigns them to threads in a predetermined manner before execution. This can reduce task management overhead but may lead to poor resource utilization if tasks are unevenly distributed.
Example with OpenMP:
#pragma omp parallel for schedule(static, 10)
for (int i = 0; i < N; i++) {
// Task processing
}
Dynamic Task Assignment
Dynamic task assignment distributes tasks to threads more flexibly during execution. This approach can better balance the load, especially when tasks have varying execution times, but it can introduce additional management overhead.
Example with OpenMP:
#pragma omp parallel for schedule(dynamic, 10)
for (int i = 0; i < N; i++) {
// Task processing
}
Software Alchemy: Turning General Problems into Embarrassingly Parallel Ones
Transforming general problems into embarrassingly parallel problems can greatly enhance parallel computing efficiency. This often involves reorganizing the problem or decomposing tasks to minimize dependencies and communication needs.
Problem Decomposition
- Decomposing into Independent Sub-Problems: Identify parts of the problem that can be executed independently and parallelize them.
Example:
- Pi Calculation: Using the Monte Carlo method to estimate π, where each sample is processed independently.
Code Example:
#include <omp.h>
#include <stdio.h>
#include <stdlib.h>
#define N 10000000
int main() {
int count = 0;
#pragma omp parallel
{
unsigned int seed = omp_get_thread_num();
#pragma omp for reduction(+:count)
for (int i = 0; i < N; i++) {
double x = (double)rand_r(&seed) / RAND_MAX;
double y = (double)rand_r(&seed) / RAND_MAX;
if (x * x + y * y <= 1) {
count++;
}
}
}
double pi = (double)count / N * 4;
printf("Estimated Pi: %f\n", pi);
return 0;
}
Eliminating Dependencies
- Reducing Data Dependencies: Modify algorithms to require less communication or synchronization between threads.
Example:
- Parallel Sorting Algorithm: Use parallel merge sort where sub-arrays are sorted independently and merged in parallel.
Code Example:
#include <omp.h>
#include <stdio.h>
#include <stdlib.h>
void merge(int* array, int left, int mid, int right) {
int n1 = mid - left + 1;
int n2 = right - mid;
int* L = malloc(n1 * sizeof(int));
int* R = malloc(n2 * sizeof(int));
for (int i = 0; i < n1; i++)
L[i] = array[left + i];
for (int j = 0; j < n2; j++)
R[j] = array[mid + 1 + j];
int i = 0, j = 0, k = left;
while (i < n1 && j < n2) {
if (L[i] <= R[j]) {
array[k++] = L[i++];
} else {
array[k++] = R[j++];
}
}
while (i < n1) {
array[k++] = L[i++];
}
while (j < n2) {
array[k++] = R[j++];
}
free(L);
free(R);
}
void merge_sort(int* array, int left, int right) {
if (left < right) {
int mid = left + (right - left) / 2;
#pragma omp task shared(array) firstprivate(left, mid)
merge_sort(array, left, mid);
#pragma omp task shared(array) firstprivate(mid, right)
merge_sort(array, mid + 1, right);
#pragma omp taskwait
merge(array, left, mid, right);
}
}
In this example:
- Merge Sort: The merge_sort function uses OpenMP tasks to sort sub-arrays in parallel.
Conclusion
Optimizing performance in parallel computing involves understanding and managing various aspects:
- Sources of Overhead: Includes communication, thread management, and synchronization overheads.
- Embarrassingly Parallel vs. Non-Embarrassingly Parallel: Identifying whether a problem can be easily parallelized or requires complex management.
- Static vs. Dynamic Task Assignment: Choosing between fixed and flexible task distribution.
- Transforming Problems: Reorganizing or decomposing problems to fit parallelism models efficiently.