OpenMP三种并行方式的对比

算例

对$\pi$的值通过级数进行计算，采用的公式为如下。

假设需要计算前N项的级数和，则$\pi$的表达式为：

$\pi \cdot N = \frac{4}{1+\frac{1}{4 \cdot N^2}} + \frac{4}{1+\frac{3^2}{4 \cdot N^2}} + \frac{4}{1+\frac{5^2}{4 \cdot N^2}} \cdots \frac{4}{1+\frac{(2N+1)^2}{4 \cdot N^2}}$

计算

分别使用OpenMP中的共享任务结构、private和critical语句、并行归约与串行程序进行计算精度和时间的对比，计算中N取值为10000000，对比结果如下：

pi : 3.14159
Seriel Process Total Time: 0.069s
pi : 2.63998
Parallel Process 1 Total Time: 0.309s
pi : 2.82509
Parallel Process 2 Total Time: 0.044s
pi : 3.14159
Parallel Process 3 Total Time: 0.035s

其中：Parallel Process 1为共享任务结构，Parallel Process 2为private和critical语句、Parallel Process 3为并行归约。

可以看出P1和P2与$\pi$的值相差较远，P3算的最精确；P1所使用的时间比串行还要多，P2和P3所使用的时间都比串行少。

对于此问题，P3是最优的选择方案。

代码

// test case of OpenMP
​
#include <iostream>
#include <omp.h>
#include <time.h>
​
using namespace std;
​
static long num_steps = 10000000;
double step;
#define NUM_THREADS 2
​
​
int SerielProcess()
{
    clock_t startTime, endTime;
    startTime = clock();
​
    int i;
    double x, pi, sum = 0.0;
    
    step = 1.0 / (double)num_steps;
    for (i = 0; i < num_steps; i++)
    {
        x = (i + 0.5)*step;
        sum += 4.0 / (1.0 + x * x);
    }
    pi = step * sum;
    cout << "pi : " << pi << endl;
​
    endTime = clock();
    cout << "Seriel Process Total Time: " << (double)(endTime - startTime) / CLOCKS_PER_SEC << "s" << endl;
    return 0;
}
​
​
// 使用共享任务结构并行化的程序
int ParallelProcess1()
{
    clock_t startTime, endTime;
    startTime = clock();
​
    int i;
    double x, pi, sum[NUM_THREADS];
    step = 1.0 / (double)num_steps;
    omp_set_num_threads(NUM_THREADS);
#pragma omp parallel
    {
        double x;
        int id;
        id = omp_get_thread_num();
        for (i = id, sum[id] = 0.0; i < num_steps; i = i + NUM_THREADS)
        {
            x = (i + 0.5)*step;
            sum[id] += 4.0 / (1.0 + x * x);
        }
    }
    for (i = 0, pi = 0.0; i < NUM_THREADS; i++)
        pi += sum[i] * step;
​
    cout << "pi : " << pi << endl;
​
    endTime = clock();
    cout << "Parallel Process 1 Total Time: " << (double)(endTime - startTime) / CLOCKS_PER_SEC << "s" << endl;
    return 0;
}
​
​
// 使用private子句和critical部分并行化的程序
int ParallelProcess2()
{
    clock_t startTime, endTime;
    startTime = clock();
​
    int i;
    double x, pi = 0.0, sum;
    step = 1.0 / (double)num_steps;
    omp_set_num_threads(NUM_THREADS);
#pragma omp parallel private(x, sum)
    {
        int id;
        id = omp_get_thread_num();
        for (i = id, sum = 0.0; i < num_steps; i = i + NUM_THREADS)
        {
            x = (i + 0.5)*step;
            sum+= 4.0 / (1.0 + x * x);
        }
#pragma omp critical
        pi += sum * step;
    }
​
    cout << "pi : " << pi << endl;
​
    endTime = clock();
    cout << "Parallel Process 2 Total Time: " << (double)(endTime - startTime) / CLOCKS_PER_SEC << "s" << endl;
    return 0;
}
​
​
// 使用并行归约得出的并行程序
int ParallelProcess3()
{
    clock_t startTime, endTime;
    startTime = clock();
​
    int i;
    double x, pi, sum = 0.0;
    step = 1.0 / (double)num_steps;
    omp_set_num_threads(NUM_THREADS);
#pragma omp parallel for reduction (+:sum) private(x)
    for (i = 0; i < num_steps; i++)
    {
        x = (i + 0.5)*step;
        sum += 4.0 / (1.0 + x * x);
    }
    pi = sum * step;
​
    cout << "pi : " << pi << endl;
​
    endTime = clock();
    cout << "Parallel Process 3 Total Time: " << (double)(endTime - startTime) / CLOCKS_PER_SEC << "s" << endl;
    return 0;
}
int main()
{
    SerielProcess();
    ParallelProcess1();
    ParallelProcess2();
    ParallelProcess3();
    system("pause");
    return 0;
}