5題每題20分1. 1）簡述MPI 6個函數(shù)格式定義，作用，參數(shù)含義。MPI簡介：消息傳遞接口的標準，用于開發(fā)基于消息傳遞的并行程序，目的是為用戶提供一個實際可用的、可移植的、高效和靈活的消息傳遞接口庫，能夠在PC Windows和所有主要的Unix工作站以及并行機上實現(xiàn)。MPI是一個庫，不是一種語言，實現(xiàn)并行必須依托于某種語言：FORTRAN， MPI主要函數(shù)：MPI_Init，初始化函數(shù)：MPI程序通過調用MPI_Init函數(shù)進行MPI環(huán)境，并完成所有的初始化工作，這個函數(shù)通常是MPI程序的第一個函數(shù)調用。 格式如下： int MPI_Init( int *argc, char *argv )MPI_Finalize，結束函數(shù)：MPI通過調用MPI_Finalize函數(shù)從MPI環(huán)境中退出，它是MPI程序的最后一個MPI函數(shù)調用，否則程序的執(zhí)行結果是不可預知的。 格式如下： int MPI_Finalize(void) ;MPI_Comm_rank，獲取進程的編號：MPI程序通過MPI_Comm_Rank函數(shù)調用獲取當前進程在指定通信域中的編號，有了該編號，不同的進程就可以將自身和其他進程區(qū)分開來，從而實現(xiàn)進程間的并行和合作。 格式如下：nt MPI_Comm_rank(MPI_Comm comm, int *rank)MPI_Comm_size，獲取指定通信域的進程數(shù)：MPI通過調用MPI_Comm_size函數(shù)獲取指定通信域的進程個數(shù)，進程可根據(jù)它來確定自己應該完成的任務比例。 格式如下：int MPI_Comm_size(MPI_Comm comm, int *size)MPI_Send消息發(fā)送函數(shù)：MPI_Send函數(shù)用于發(fā)送一個消息到目標進程。其格式如下： int MPI_Send( void *buf, int count, MPI_Datatype datatype, int dest, int tag, MPI_Comm_comm)buf : 消息發(fā)送的起始地址count ：發(fā)送消息的數(shù)量datatype: 發(fā)送數(shù)據(jù)的類型dest: 標識目標進程tag: 發(fā)送消息時打上的標簽comm: 通信類型MPI_Recv，消息接收：MPI_Recv函數(shù)用于從指定進程接收一個消息，格式如下：int MPI_Recv( void *buf, int count, MPI_Datatype datatype, int source, int tag, MPI_Comm, comm, MPI_Status *status )buf : 消息接收后存放地址count : 接收數(shù)量datatype : 接收數(shù)據(jù)類型source : 發(fā)送消息的進程tag : 消息的標簽comm : 通信類型status : 接收狀態(tài)1.2）舉例簡單的應用解釋如何通信。每個進程會屬于一個或多個通信域。一個簡單的例子/* simple.c */#include “mpi.h” /*MPI頭文件*/#include int main(argc, argv)int argc ;char *argv ; int rank, size, tag = 1 ; int senddata, recvdata ; MPI_Status status ; MPI_Init( &argc, &argv ) ; /*MPI的初始化*/ MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; /*該進程的編號 */ MPI_Comm_size( MPI_COMM_WORLD, &size ); /* 總的進程數(shù)目*/if ( rank = 0 ) int senddata, recvdata ; MPI_Status status ; MPI_Init( &argc, &argv ) ; /*MPI的初始化*/ MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; /*該進程的編號 */ MPI_Comm_size( MPI_COMM_WORLD, &size ); /* 總的進程數(shù)目*/ if ( rank = 0 ) senddata = 9999 ; MPI_Send( &senddata, 1, MPI_INT, 1, tag, MPI_COMM_WORLD ) ; /* 發(fā)送數(shù)據(jù)到進 程1 */ if ( rank = 1 ) MPI_Recv( &recvdata, 1, MPI_INT, 0, tag, MPI_COMM_WORLD, &status); /*從進程0接收數(shù)據(jù)*/ MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ;另一個例子實現(xiàn) sum( a + b )，并且把求和結果打印出來。這里 a, b 都是n維空間的向量，并且每個元素都為整數(shù)。#include “mpi.h” /*MPI頭文件*/#include #include int main(argc, argv)int argc ;char *argv ; int rank, size, i, tag = 1 ; int *a, *b, n; n = 100 ; a = (int*)malloc( sizeof( int ) * n ) ; b = (int*)malloc( sizeof( int ) * n ) ; for(i = 0 ; i n ; i+) ai = 1 ; bi = 2 ; MPI_Status status ; MPI_Init( &argc, &argv ) ; /*MPI的初始化*/ MPI_Comm_size( MPI_COMM_WORLD, &size ); /* 總的進程數(shù)目*/ int nSize = n / size ; MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; /*該進程的編號 */ if( rank != (size - 1) ) int sum = 0 ; for( i = 0 ; i nSize ; i+ ) sum += ai + rank * nSize + b i + rank * nSize ; MPI_Send( &sum, 1, MPI_INT, (size-1), tag, MPI_COMM_WORLD ) ; /* 發(fā)送求和數(shù)據(jù)到進程(size-1) */else int sum = 0, total = 0 ; for( i = (size - 1) * nSize ; i n ; i+ ) sum += ai + bi ; total += sum ; for( i = 0 ; i (size - 1) ; i+ ) MPI_Recv( &sum, 1, MPI_INT, i, tag, MPI_COMM_WORLD, &status); /*從各個進程接收部分求和數(shù)據(jù)*/ total += sum ; printf( total = %dn, total ) ; MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ;2. 1）通過MPI如何實現(xiàn)2個矢量相加。/* simple.c */#include /*MPI頭文件*/#include #include int main(argc, argv)int argc ;char *argv ; int rank, size, tag = 1 ; int *a, *b , n = 100 ; a = (int*)malloc( sizeof( int ) * n ) ; b = (int*)malloc( sizeof( int ) * n ) ; int i ; for( i = 0 ; i n ; i+ ) ai = 1 ; bi = 2 ; MPI_Status status ; MPI_Init( &argc, &argv ) ; /*MPI的初始化*/ MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; /*該進程的編號 */ MPI_Comm_size( MPI_COMM_WORLD, &size ); /* 總的進程數(shù)目*/ int nSize = n / size ; int sum ; if( rank (size -1) ) sum = 0 ; for( i = 0 ; i nSize ; i+ ) sum += ai + bi ; else sum = 0 ; for( i = nSize * (size - 1) ; i n ; i+ ) sum += ai + bi ; printf(cpu = %d, sum = %dn, rank, sum ) ; MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ;2.2）通過MPI如何實現(xiàn)2個矢量相乘。#include /*MPI頭文件*/#include #include int main(argc, argv)int argc ;char *argv ; int rank, size; int n = 100 ; int i ; MPI_Status status ; MPI_Init( &argc, &argv ) ; MPI_Comm_size( MPI_COMM_WORLD, &size ); int nSize = n / size ; MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; int *a, *b ; a = (int*)malloc( sizeof(int) * n ) ; b = (int*)malloc( sizeof(int) * n ) ; int( i = 0 ; i n ; i+ ) ai = 1 ; bi = 2 ; int tag = 1 ; if( rank != (size - 1) ) int sum = 0 ; for( i = 0 ; i nSize ; i+ ) sum += arank * nSize + i* brank * nSize + i; MPI_Send( &sum, 1, MPI_INT, (size-1), tag, MPI_COMM_WORLD ) ; else int sum = 0, total = 0 ; for( i = (size - 1) * nSize ; i n ; i+ ) sum += ai * bi; total += sum ; for( i = 0 ; i (size - 1) ; i+ ) MPI_Recv( &sum, 1, MPI_INT, i, tag, MPI_COMM_WORLD, &status); total += sum ; printf( total = %dn, total ) ; MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ; 3.1）n!如何用并行計算做（n給定）#include stdio.h#include stdlib.h#include math.h#include mpi.hint m,N;long jiech;int my_rank;int p;MPI_Status status;/* * 函數(shù)名: main * 輸入：argc為命令行參數(shù)個數(shù)； * argv為每個命令行參數(shù)組成的字符串數(shù)組。 * 輸出：返回0代表程序正常結束 */int main(int argc, char *argv) int i,my_rank,group_size; long lji=1; MPI_Init(&argc,&argv); /* 啟動計算 */ MPI_Comm_size(MPI_COMM_WORLD,&group_size); /* 找進程數(shù) */ MPI_Comm_rank(MPI_COMM_WORLD,&my_rank); /* 找自己的id */ p=group_size; if(my_rank=0) printf(Please input DATA:);scanf(%d,&N);MPI_Bcast(&N,1,MPI_INT,0,MPI_COMM_WORLD); /* 廣播size到所有進程*/ for(i=my_rank;iN;i=i+p) lji=lji*(i+1); /* 求各個處理器中l(wèi)ji積，并將最終結果存放在0進程的jiech中*/ MPI_Reduce(&lji,&jiech,1,MPI_INT,MPI_PROD,0,MPI_COMM_WORLD); if (my_rank=0) /* 打印結果*/ printf(N! =%d,jiech); printf(n); / printf(Whole running time = %f secondsn,time2-starttime); MPI_Barrier(MPI_COMM_WORLD); /* 同步所有進程 */ MPI_Finalize(); /* 結束計算 */ return (0);3.2） 1+2+3+.+n如何用并行計算做（n給定，例子中n=100）#include /*MPI頭文件*/#include #include int main(argc, argv)int argc ;char *argv ; int rank, size; int n = 100 ;int i ; MPI_Status status ; MPI_Init( &argc, &argv ) ; MPI_Comm_size( MPI_COMM_WORLD, &size ); int nSize = n / size ; MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; int tag = 1 ; if( rank != (size - 1) ) int sum = 0 ; for( i = 0 ; i nSize ; i+ ) sum += rank * nSize + i + 1; MPI_Send( &sum, 1, MPI_INT, (size-1), tag, MPI_COMM_WORLD ) ; elseint sum = 0, total = 0 ; for( i = (size - 1) * nSize ; i n ; i+ ) sum += i + 1; total += sum ; for( i = 0 ; i (size - 1) ; i+ ) MPI_Recv( &sum, 1, MPI_INT, i, tag, MPI_COMM_WORLD, &status); total += sum ; printf( total = %dn, total ) ; MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ; 4.1）不同的壓縮矩陣如何實現(xiàn)矩陣乘。4.2） 給你一個矩陣，讓你寫出三種格式中的一種存儲（寫出三種壓縮方式中的一種，矩陣和矢量乘你怎么做壓縮及如何存儲）16稀疏矩陣矢量乘(CSR)for(int i = 0 ; i n ; i+ ) int row_s = ptri ; int row_e = ptri+1 ; double sum = 0.0 ;for(int j = row_s ; j row_e ; j+)sum+=dataj*xindicesj; bi = sum ;稀疏矩陣矢量乘(DIA)for(int i = 0 ; i n ; i+)double sum = 0.0 ; for(int j = 0 ; j =0 & ncol n )double val = datai+j*n; sum += val * xncol ; bi = sum ;稀疏矩陣矢量乘(ELL)for(int i = 0 ; i n ; i+) double sum = 0.0 ;for(int j = 0 ; j cols; j+)double val = datai + j*n ; if( val != 0 )sum += val*xindicesi+j*n ; bi = sum ;#include /*MPI頭文件*/#include #include int main(argc, argv)int argc ;char *argv ; int rank, size; double *data ; int *indices, *ptr ; double *b, *x ; data = (double*)malloc( sizeof( double ) * SIZE * 5 ) ; indices = (int*)malloc( sizeof( int ) * SIZE * 5 ) ; ptr = (int*)malloc( sizeof( int ) * (SIZE + 1) ) ; x = (double*)malloc( sizeof( double ) * SIZE ) ; b = (double*)malloc( sizeof( double ) * SIZE ) ; csr_scalar_sparse_matrix_cpu(data, indices, ptr) ;int i, j, k ;for( k = 0 ; k SIZE ; k+ )xk = 1.0 ; int i ; MPI_Status status ; MPI_Init( &argc, &argv ) ; MPI_Comm_size( MPI_COMM_WORLD, &size ); int nSize = n / size ; MPI_Comm_rank( MPI_COMM_WORLD, &rank ) ; int tag = 1 ; if( rank != (size - 1) ) for( i = 0 ; i nSize ; i+ ) int r_start = ptri + nSize * rank ;int r_end = ptri + 1 + nSize * rank ;double sum = 0.0 for( j = r_start ; j r_end ; j+ ) sum += dataj * xindicesj ; bi + nSize * rank = sum ; MPI_Send(b+rank*nSize, nSize, MPI_DOUBLE, (size-1), tag, MPI_COMM_WORLD ) ; if( rank = (size -1 ) ) for( i = 0 ; i (size - 1) ; i+ ) MPI_Recv( b + i * nSize, nSize, MPI_DOUBLE, i, tag, MPI_COMM_WORLD, &status); double sum = 0.0 ; for( i = 0 ; i SIZE ; i+ ) sum += bi ; printf( sum = %lfn, sum ) ; MPI_Finalize() ; /*MPI的結束函數(shù)*/ return (0) ; 5）GPU,范式，平方和3、#include #include #include #include #define SIZE 1048576#define BLOCK_NUM 32#define THREAD_NUM 256_global_ void sumOfSquares_gpu0( float *a, int n, float *result )int tid = threadIdx.x ;int bid = blockIdx.x ;float sum = 0.0 ;for( int i = bid * THREAD_NUM + tid ; i n ; i += BLOCK_NUM * THREAD_NUM )sum += ai * ai ;resultbid * THREAD_NUM + tid = sum ;int main( int argc, char *argv )cudaEvent_t start, stop ;float elapsedTime ;float *result, *dev_result, *a, *dev_a ;cudaMalloc( (void*)&dev_result, BLOCK_NUM * THREAD_NUM * sizeof(float) ) ;cudaMalloc( (void*)&dev_a, SIZE * sizeof(float) ) ;a = (float*)malloc( SIZE * sizeof( float ) ) ;result = (float*)malloc( BLOCK_NUM * THREAD_NUM * sizeof( float ) ) ;for( int i = 0 ; i SIZE ; i+ )ai = 1.0 ;cudaMemcpy(dev_a, a, SIZE * sizeof(float), cudaMemcpyHostToDevice ) ;cudaEventCreate( &start ) ;cudaEventCreate( &stop ) ;cudaEventRecord( start, 0 ) ;sumOfSquares_gpu0( dev_a, SIZE, dev_result ) ;cudaMemcpy(result, dev_result, BLOCK_NUM * THREAD_NUM * sizeof(float), cudaMemcpyDeviceToHost ) ; double sum = 0.0 ; for(int i = 0 ; i BLOCK_NUM * THREAD_NUM ; i+ ) sum += resulti ; cudaEventRecord( stop, 0 ) ; cudaEventSynchronize( stop ) ; cudaEventElapsedTime( &elapsedTime, start, stop ) ; printf( TotalTime = : %20.12f ms n , elapsedTime ) ; printf( sum = : %20.12fn , sum ) ; cudaEventDestroy( start ) ; cudaEventDestroy( stop ) ; free( a ) ; cudaFree( dev_a ) ; cudaFree( dev_result ) ; return 0 ;2、#include #include #include #include #define SIZE 1048576#define BLOCK_NUM 32#define THREAD_NUM 256_global_ void sumOfSquares_gpu0( float *a, int n, float *result )_shared_ float sharedTHREAD_NUM;int tid = threadIdx.x ;int bid = blockIdx.x ;sharedtid = 0.0 ;for( int i = bid * THREAD_NUM + tid ; i n ; i += BLOCK_NUM * THREAD_NUM )sharedtid += ai * ai ; _syncthreads(); if(tid = 0) for(int i = 1; i THREAD_NUM; i+) shared0 += sharedi; resultbid = shared0; int main( int argc, char *argv )cudaEvent_t start, stop ;float elapsedTime ;float *result, *dev_result, *a, *dev_a ;cudaMalloc( (void*)&dev_result, BLOCK_NUM * sizeof(float) ) ;cudaMalloc( (void*)&dev_a, SIZE * sizeof(float) ) ;a = (float*)malloc( SIZE * sizeof( float ) ) ;result = (float*)malloc( BLOCK_NUM * sizeof( float ) ) ;for( int i = 0 ; i SIZE ; i+ )ai = 1.0 ;cudaMemcpy(dev_a, a, SIZE * sizeof(float), cudaMemcpyHostToDevice ) ;cudaEventCreate( &start ) ;cudaEventCreate( &stop ) ;cudaEventRecord( start, 0 ) ;sumOfSquares_gpu0( dev_a, SIZE, dev_result ) ;cudaMemcpy(result, dev_result, BLOCK_NUM * sizeof(float), cudaMemcpyDeviceToHost ) ; double sum = 0.0 ; for(int i = 0 ; i BLOCK_NUM ; i+ ) sum += resulti ; cudaEventRecord( stop, 0 ) ; cudaEventSynchronize( stop ) ; cudaEventElapsedTime( &elapsedTime, start, stop ) ; printf( TotalTime = : %20.12f ms n , elapsedTime ) ; printf( sum = : %20.12fn , sum ) ; cudaEventDestroy( start ) ; cudaEventDestroy( stop ) ; free( a ) ; cudaFree( dev_a ) ; cudaFree( dev_result ) ; return 0 ;1、#include #include #include #include #define SIZE 1048576#define THREAD_NUM 256_global_ void sumOfSquares_gpu0( float *a, int n, float *result )int tid = threadIdx.x ;float sum = 0.0 ;for( int i = tid ; i n ; i += THREAD_NUM )sum += ai * ai ;resulttid = sum ;int main( int argc, char *argv )cudaEvent_t start, stop ;float elapsedTime ;float *result, *dev_result, *a, *dev_a ;cudaMalloc( (void*)&dev_result, THREAD_NUM * sizeof(float) ) ;cudaMalloc( (void*)&dev_a, SIZE * sizeof(float) ) ;a = (float*)malloc( SIZE * sizeof( float ) ) ;result = (float*)malloc( THREAD_NUM * sizeof( float ) ) ;for( int i = 0 ; i SIZE ; i+ )ai = 1.0 ;cudaMemcpy(dev_a, a, SIZE * sizeof(float), cudaMemcpyHostToDevice ) ;cudaEventCreate( &start ) ;cudaEventCreate( &stop ) ;cudaEventRecord( start, 0 ) ;sumOfSquares_gpu0( dev_a, SIZE, dev_result ) ;cudaMemcpy(result, dev_result, THREAD_NUM * sizeof(float), cudaMemcpyDeviceToHost ) ; double sum = 0.0 ; for(int i = 0 ; i THREAD_NUM ; i+ ) sum += resulti ; cudaEventRecord( stop, 0 ) ; cudaEventSynchronize( stop ) ; cudaEventElapsedTime( &elapsedTime, start, stop ) ; printf( TotalTime = : %20.12f ms n , elapsedTime ) ; printf( sum = : %20.12fn , sum ) ; cudaEventDestroy( start ) ; cudaEventDestroy( stop ) ; free( a ) ; cudaFree( dev_a ) ; cudaFree( dev_result ) ; return 0 ;4、#include #include #include #include #define SIZE 1048576#define BLOCK_NUM 32#define THREAD_NUM 256_global_ void sumOfSquares_gpu0( float *a, int n, float *resul