并行程序设计——MPI编程

并行程序设计——MPI编程

实验一

题目描述

实现第5章课件中的梯形积分法的MPI编程熟悉并掌握MPI编程方法，规模自行设定，可探讨不同规模对不同实现方式的影响。

实验代码

# include 
#include 
#include 

double totalSize = 0.00;//表示总面积
double gap = 0.00;
int total_num = 1000;
double begin_num = 1.000, end_num = 8.0000;

int min(int i, int num);

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

double cal(int begin, int size) {
    double temp_size = 0.00;
    for (int i = begin; i < min(begin + size, total_num); ++i) {
        temp_size += (f(begin_num + gap * i) + f(begin_num + gap * (i + 1))) * gap / 2;
    }
    return temp_size;
}

int min(int i, int num) {
    if (i < num) {
        return i;
    }
    return num;
}


void accept_task(int thread_num) {
}

int main(int argc, char *argv[]) {
    double buf[10];
    gap = (end_num - begin_num) / total_num;
    int rank, thread_num;
    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &thread_num);
    //每个线程都分配这么(size*rand)多个任务,主线程不分配
    int each_thread_size = total_num / (thread_num - 1) + 1;
    if (rank != 0) {
        buf[rank] = cal((rank - 1) * each_thread_size, each_thread_size);
        MPI_Send(buf + rank, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);
    }
    if (rank == 0) {
        for (int i = 1; i < thread_num; ++i) {
            double temp_size;
            MPI_Recv(&temp_size, 1, MPI_DOUBLE, i, 0, MPI_COMM_WORLD, MPI_STATUS_IGNORE);
            totalSize += temp_size;
        }
        printf("total size: %lf\n", totalSize);
    }
    MPI_Finalize();
    return MPI_SUCCESS;
}

不同规模下的实验结果

1. 当规模为1000时

2. 当规模为3000时

3. 当规模为5000时

实验结论

有上述实验结果可知,当规模越大时,计算的数据越加精确

实验二

实验内容

对于课件中“多个数组排序”的任务不均衡案例进行MPI编程实现，规模可自己设定、调整。

实验代码

#include 
#include 
#include 
#include 
#include
#include 

using namespace std;

const int ARR_NUM = 100; //固定数组大小
const int ARR_LEN = 4000; //固定数组长度
int seg = 50; //粗颗粒的分配大小
vector<vector<int> > arr(ARR_NUM, vector<int>(ARR_LEN));

void init() {
    for (int i = 0; i < ARR_NUM; i++) {
        for (int j = 0; j < ARR_LEN; j++)
            arr[i][j] = rand() % 100;
    }
}

void doTask(int begin) {
    for (int i = begin; i < min(begin + seg, ARR_NUM); ++i) {
        sort(arr[i].begin(), arr[i].end());
    }
}


int main() {
    init();
    int current_task = 0;//当前的任务
    MPI_Init(NULL, NULL);
    int rank, thread_num;
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &thread_num);
    MPI_Status status;
    int ready;
    bool done = false;
    if (rank == 0) {
        while (current_task < ARR_NUM) {
            //接受任何一个线程的状态
            MPI_Recv(&ready, 1, MPI_INT, MPI_ANY_SOURCE, MPI_ANY_TAG, MPI_COMM_WORLD, &status);
            MPI_Send(&current_task, 1, MPI_INT, status.MPI_SOURCE, 0, MPI_COMM_WORLD);
            current_task += seg;
        }
        cout << "all work done!!!!!" << endl;
        done = true;
    } else {
        while (!done) {
            int begin;
            MPI_Send(&ready, 1, MPI_INT, 0, 0, MPI_COMM_WORLD);
            MPI_Recv(&begin, 1, MPI_INT, 0, 0, MPI_COMM_WORLD, &status);
            doTask(begin);
        }
    }
    MPI_Finalize();
    return 0;
}

实验结果

可以发现成功排序

实验三(附加题)

实验内容

实现高斯消去法解线性方程组的MPI编程，与SSE（或AVX）编程结合，并与Pthread、OpenMP（结合SSE或AVX）版本对比，规模自己设定。

实验代码

#include 
#include 
#include 
#include 
#include 


const int n = 1024;//固定矩阵规模，控制变量
const int maxN = n + 1; // 矩阵的最大值
float a[maxN][maxN];
float temp[maxN][maxN];//用于暂时存储a数组中的变量，控制变量唯一
int next_task = 0;
int seg;
int line = 0;//记录当前所依赖的行数
struct timeval startTime, stopTime;// timers


/**
 * 根据第i行的元素，消除j行的元素
 * @param i 根据的行数
 * @param j 要消元的行数
 */
void OMP_elimination(int i, int j) {
    //求出相差倍数
    float temp = a[j][i] / a[i][i];
    //遍历这一行的所有值，将i后面的数值依次减去相对应的值乘以倍数
    for (int k = i + 1; k <= n; ++k) {
        a[j][k] -= a[i][k] * temp;
    }
    //第i个为0
    a[j][i] = 0.00;
}


//用于矩阵改变数值,为防止数据溢出,随机数的区间为100以内的浮点数
void change() {
    srand((unsigned) time(NULL));
    for (int i = 0; i < n; i++) {
        for (int j = 0; j <= n; j++) {
            a[i][j] = (float) (rand() % 10000) / 100.00;
        }
    }
}


int main(int argc, char *argv[]) {
    change();
    int rank, thread_num;
    gettimeofday(&startTime, NULL);
    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &thread_num);
    MPI_Status status;
    int ready;
    bool done = false;
    if (rank == 0) {
        printf("size : %d\n", n);
        for (line = 0; line < n - 1; ++line) {
            next_task = line + 1;
            seg = (n - next_task) / (thread_num - 1) + 1;
            for (int i = 1; i < thread_num; i++) {
                int task = (i - 1) * seg + next_task;
                MPI_Send(&task, 1, MPI_INT, i, 0, MPI_COMM_WORLD);
            }
            //等待所有线程
            for (int j = 1; j < thread_num; ++j) {
                MPI_Recv(&ready, 1, MPI_INT, MPI_ANY_SOURCE, 0, MPI_COMM_WORLD, &status);
            }
        }
        printf("all work done!!!!!\n");
        done = true;
        gettimeofday(&stopTime, NULL);
        double trans_mul_time =
                (stopTime.tv_sec - startTime.tv_sec) * 1000 + (stopTime.tv_usec - startTime.tv_usec) * 0.001;
        printf("time: %lf ms\n", trans_mul_time);
    } else {
        while (!done) {
            int task;
            MPI_Recv(&task, 1, MPI_INT, 0, 0, MPI_COMM_WORLD, &status);
            int min = task + seg < n ? task + seg : n;
            for (int i = task; i < min; ++i) {
                OMP_elimination(line, i);
            }
            MPI_Send(&ready, 1, MPI_INT, 0, 0, MPI_COMM_WORLD);
        }
    }
    MPI_Finalize();
    return 0;
}

实验结果

当规模为512时

当规模为1024时

当规模为2048时