梯形积分法【OpenMP实现】多个版本

浅浅的花香味﹌ 2022-04-03 08:28 186阅读 0赞

## 简述 ##

会用多个版本来写。操作是用命令行来操作。  
除了第二版本是在内容上基于第一个版本的完善，其他都是降低算法的复杂程度的，可以放心阅读

### 文章目录 ###

*   *  简述
     *  版本1
     *  版本2
     *  版本3
     *  版本4

## 版本1 ##

*  **要求n被thread\_count整除** 不然可以会有计算错误。

#include <iostream>
    #include <omp.h>
    
    #define FUN(x) (x * x)
    
    using namespace std;
    #pragma warning(disable : 4996)
    void Trap(double a, double b, int n, double *global_result_p);
    int main(int argc, char **argv) { 
    	if (argc < 5) return 0;
    	double global_result = 0.0;
    	double a, b;
    	int n;
    	int thread_count = strtol(argv[1], NULL, 10);
    	a = strtod(argv[2], NULL);
    	b = strtod(argv[3], NULL);
    	n = strtol(argv[4], NULL, 10);
    
    	// n 必须被 thread_count 整除
    #pragma omp parallel num_threads (thread_count)
    	Trap(a, b, n, &global_result);
    
    	cout << "With n = " << n << " trapzoids, our estimate\n";
    	cout << "of the integral from " << a << " to " << b <<" = "<< global_result<< endl;
    }
    
    void Trap(double a, double b, int n, double *global_result_p) { 
    	double h, x, my_result;
    	double local_a, local_b;
    	int i, local_n;
    	int my_rank = omp_get_thread_num();
    	int thread_count = omp_get_num_threads();
    
    	h = (b - a) / n;
    	local_n = n / thread_count;  // same in all threads
    	local_a = a + my_rank * local_n * h;
    	local_b = local_a + local_n * h;
    	x = local_a; // initial x
    	my_result = (FUN(local_a) + FUN(local_b)) / 2;
    	for (i = 1; i < local_n; ++i) { 
    		x += h;
    		my_result += FUN(x);
    	}
    	my_result *= h;
    # pragma omp critical 
    	*global_result_p += my_result;
    }

编译好源文件之后，就用下面的命令执行

*  这里是用4个线程，来计算在0，1区间上的 x 2 x^2 x2的用n=64划分的梯形积分公式。结果接近1/3 可以通过提高n来提高精度。**但这个版本只能计算n为thread\_count的整数倍的时候**

PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 64
    With n = 64 trapzoids, our estimate
    of the integral from 0 to 1 = 0.333374

## 版本2 ##

*  可以使用不被thread\_count整除的n
 *  **改进代码：** 添加了一个变量left表示剩余。剩余的让前left个线程每个再多算点。（一般来说线程数目都会比n要小很多。（不然在算法上就会不精确（**n不够大的话**）。））

left = n % thread_count;
    if (my_rank < left) local_n += 1;
    if (my_rank < left){  local_a = a + my_rank * local_n * h; }
    else {  local_a = a + left * (local_n + 1) * h + (my_rank - left) * local_n * h; }

实际的代码:

#include <iostream>
    #include <omp.h>
    
    #define FUN(x) (x * x)
    
    using namespace std;
    #pragma warning(disable : 4996)
    void Trap(double a, double b, int n, double *global_result_p);
    int main(int argc, char **argv) { 
    	if (argc < 5) return 0;
    	double global_result = 0.0;
    	double a, b;
    	int n;
    	int thread_count = strtol(argv[1], NULL, 10);
    	a = strtod(argv[2], NULL);
    	b = strtod(argv[3], NULL);
    	n = strtol(argv[4], NULL, 10);
    
    #pragma omp parallel num_threads (thread_count)
    	Trap(a, b, n, &global_result);
    
    	cout << "With n = " << n << " trapzoids, our estimate\n";
    	cout << "of the integral from " << a << " to " << b <<" = "<< global_result<< endl;
    }
    
    void Trap(double a, double b, int n, double *global_result_p) { 
    	double h, x, my_result;
    	double local_a, local_b;
    	int i, local_n, left;
    	int my_rank = omp_get_thread_num();
    	int thread_count = omp_get_num_threads();
    
    	h = (b - a) / n;
    
    	local_n = n / thread_count;  // same in all threads
    	left = n % thread_count;
    	if (my_rank < left) local_n += 1;
    	if (my_rank < left){  local_a = a + my_rank * local_n * h; }
    	else {  local_a = a + left * (local_n + 1) * h + (my_rank - left) * local_n * h; }
    
    	local_b = local_a + local_n * h;
    	x = local_a; // initial x
    	my_result = (FUN(local_a) + FUN(local_b)) / 2;
    	for (i = 1; i < local_n; ++i) { 
    		x += h;
    		my_result += FUN(x);
    	}
    	my_result *= h;
    # pragma omp critical 
    	*global_result_p += my_result;
    }

发现精度不断的提升，在只改变n的数目的情况下。

PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 64
    With n = 64 trapzoids, our estimate
    of the integral from 0 to 1 = 0.333374
    PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 65
    With n = 65 trapzoids, our estimate
    of the integral from 0 to 1 = 0.333373
    PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 66
    With n = 66 trapzoids, our estimate
    of the integral from 0 to 1 = 0.333372
    PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 67
    With n = 67 trapzoids, our estimate
    of the integral from 0 to 1 = 0.33337

## 版本3 ##

*  对于部分对指针不太熟的人来说，我们可以做出下面的改进
 *  **修改部分：**

#pragma omp parallel num_threads (thread_count)
    	{ 
    		double my_result = Trap(a, b, n);
    #pragma omp critical 
    		global_result += my_result;
    	}

#include <iostream>
    #include <omp.h>
    
    #define FUN(x) (x * x)
    
    using namespace std;
    #pragma warning(disable : 4996)
    double Trap(double a, double b, int n);
    int main(int argc, char **argv) { 
    	if (argc < 5) return 0;
    	double global_result = 0.0;
    	double a, b;
    	int n;
    	int thread_count = strtol(argv[1], NULL, 10);
    	a = strtod(argv[2], NULL);
    	b = strtod(argv[3], NULL);
    	n = strtol(argv[4], NULL, 10);
    
    
    #pragma omp parallel num_threads (thread_count)
    	{ 
    		double my_result = Trap(a, b, n);
    #pragma omp critical 
    		global_result += my_result;
    	}
    
    	cout << "With n = " << n << " trapzoids, our estimate\n";
    	cout << "of the integral from " << a << " to " << b <<" = "<< global_result<< endl;
    }
    
    double Trap(double a, double b, int n) { 
    	double h, x, my_result;
    	double local_a, local_b;
    	int i, local_n, left;
    	int my_rank = omp_get_thread_num();
    	int thread_count = omp_get_num_threads();
    
    	h = (b - a) / n;
    
    	local_n = n / thread_count;  // same in all threads
    	left = n % thread_count;
    	if (my_rank < left) local_n += 1;
    	if (my_rank < left){  local_a = a + my_rank * local_n * h; }
    	else {  local_a = a + left * (local_n + 1) * h + (my_rank - left) * local_n * h; }
    
    	local_b = local_a + local_n * h;
    	x = local_a; // initial x
    	my_result = (FUN(local_a) + FUN(local_b)) / 2;
    	for (i = 1; i < local_n; ++i) { 
    		x += h;
    		my_result += FUN(x);
    	}
    	my_result *= h;
    	return my_result;
    }

结果

PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 67
    With n = 67 trapzoids, our estimate
    of the integral from 0 to 1 = 0.33337
    PS D:\C++\VS\repo\OpenMP-TEST\Debug> ./OpenMP-TEST 4 0 1 68
    With n = 68 trapzoids, our estimate
    of the integral from 0 to 1 = 0.333369
    PS D:\C++\VS\repo\OpenMP-TEST\Debug>

## 版本4 ##

*  使用规约变量和规约操作
 *  会让代码更加简单

#pragma omp parallel num_threads (thread_count) reduction(+:global_result)
    	{ 
    		global_result += Trap(a, b, n);
    	}

*  跟版本3是一样的。就是让代码更加简单了而已，用了map-reduce的思路
 *  `reduction(<operator>: <variable list>)` 前面的放操作符，后面的设置变量。
 *  但是有需要注意的，如果是减法就需要小心了。在每个线程上确实是使用了减法，但是全局上也是可能做了减法，(例如 `-1 - (-5)= 4`）这样的事情是有可能发生的。**一般来说，满足交换律的都不用担心这点hh**

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