采用Local_trap改写梯形积分的OpenMP并行程序： 1) double Local_trap(double a, double b, int n); 2) 利用critical和reduction两种方式保护临界区

1) 采用Local_trap改写梯形积分的OpenMP并行程序：

#include <iostream>
#include <omp.h>

double f(double x) {
    return x * x;
}

double Local_trap(double a, double b, int n) {
    double h = (b - a) / n;
    double sum = 0.0;
    #pragma omp parallel for reduction(+:sum)
    for (int i = 1; i < n; i++) {
        sum += f(a + i * h);
    }
    sum += (f(a) + f(b)) / 2.0;
    sum *= h;
    return sum;
}

int main() {
    double a = 0.0, b = 1.0;
    int n = 10000000;
    double result_seq = Local_trap(a, b, n);
    double result_par = Local_trap(a, b, n);
    std::cout << "Sequential result: " << result_seq << std::endl;
    std::cout << "Parallel result: " << result_par << std::endl;
    return 0;
}

2) 利用critical和reduction两种方式保护临界区：

- 使用critical关键字：

#include <iostream>
#include <omp.h>

double f(double x) {
    return x * x;
}

double Local_trap(double a, double b, int n) {
    double h = (b - a) / n;
    double sum = 0.0;
    #pragma omp parallel
    {
        double local_sum = 0.0;
        #pragma omp for
        for (int i = 1; i < n; i++) {
            local_sum += f(a + i * h);
        }
        #pragma omp critical
        sum += local_sum;
    }
    sum += (f(a) + f(b)) / 2.0;
    sum *= h;
    return sum;
}

int main() {
    double a = 0.0, b = 1.0;
    int n = 10000000;
    double result_seq = Local_trap(a, b, n);
    double result_par = Local_trap(a, b, n);
    std::cout << "Sequential result: " << result_seq << std::endl;
    std::cout << "Parallel result: " << result_par << std::endl;
    return 0;
}

- 使用reduction关键字：

#include <iostream>
#include <omp.h>

double f(double x) {
    return x * x;
}

double Local_trap(double a, double b, int n) {
    double h = (b - a) / n;
    double sum = 0.0;
    #pragma omp parallel for reduction(+:sum)
    for (int i = 1; i < n; i++) {
        sum += f(a + i * h);
    }
    sum += (f(a) + f(b)) / 2.0;
    sum *= h;
    return sum;
}

int main() {
    double a = 0.0, b = 1.0;
    int n = 10000000;
    double result_seq = Local_trap(a, b, n);
    double result_par = Local_trap(a, b, n);
    std::cout << "Sequential result: " << result_seq << std::endl;
    std::cout << "Parallel result: " << result_par << std::endl;
    return 0;
}