Parallel Programming in MPI part 3 January 25, 2011 1

Sample of the correct code for the last week's report. #include <stdio.h> #include <stdlib.h> #include <sys/time.h> #include "mpi.h" #define N 1000 int main(int argc, char *argv[]) { double *a, *b, local_c, c, r, *temp; int i, p, myid, procs, local_size; struct timeval tv; MPI_Status status; MPI_Init(&argc, &argv); MPI_Comm_size(MPI_COMM_WORLD, &procs); MPI_Comm_rank(MPI_COMM_WORLD, &myid); local_size = N/procs; a = (double *)malloc(local_size * sizeof(double)); b = (double *)malloc(local_size * sizeof(double)); if (myid == 0){ gettimeofday(&tv, NULL); srand(tv.tv_usec); for (i = 0; i < local_size; i++){ r = rand(); a[i]=r/RAND_MAX; } b[i]=r/RAND_MAX; temp = (double *)malloc(local_size * sizeof(double)); for (p = 1; p < procs; p++){ temp[i]=r/RAND_MAX; MPI_Send(temp, local_size, MPI_DOUBLE, p, 0, MPI_COMM_WORLD); for (i = 0; i < local_size; i++){ r = rand(); temp[i]=r/RAND_MAX; } } else{ MPI_Recv(a, local_size, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD, &status); MPI_Recv(b, local_size, MPI_DOUBLE, 0, 0, local_c = 0.0; for (i = 0; i < local_size; i++) local_c = local_c + a[i]*b[i]; MPI_Reduce(&local_c, &c, 1, MPI_DOUBLE, MPI_SUM, 0, if (myid == 0) printf("Result: %e \n", c); free(a); free(b); free(temp); MPI_Barrier(MPI_COMM_WORLD); MPI_Finalize();

An answer that uses MPI_Bcast #include <stdio.h> #include <stdlib.h> #include <sys/time.h> #include "mpi.h" #define N 1000 int main(int argc, char *argv[]) { double *a, *b, c, sum, r; double t1, t2; int i; int myid,procs; struct timeval tv; a = (double *)malloc(N * sizeof(double)); b = (double *)malloc(N * sizeof(double)); c = 0.0; MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &myid); MPI_Comm_size(MPI_COMM_WORLD, &procs); MPI_Barrier(MPI_COMM_WORLD); if(0 == myid){ t1 = MPI_Wtime(); gettimeofday(&tv, NULL); srand(tv.tv_usec); for (i = 0; i < N; i++){ r = rand(); a[i]=r/RAND_MAX; } b[i]=r/RAND_MAX; MPI_Bcast(a, N, MPI_DOUBLE, 0, MPI_COMM_WORLD); MPI_Bcast(b, N, MPI_DOUBLE, 0, MPI_COMM_WORLD); for (i = (N/procs)*myid; i < (N/procs)*(myid+1); i++){ c = c + a[i]*b[i]; } MPI_Reduce(&c, &sum, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD); MPI_Barrier(MPI_COMM_WORLD); if(0 == myid){ t2 = MPI_Wtime(); printf("Result: %e\n", sum); printf("number of processes:%d\n",procs); printf("Elapsed time: %e sec.\n", t2 - t1); free(a); free(b); MPI_Finalize(); Compare to the previous slide: - The structure of the program is simpler. - Consumes more memory. - Does more amount of communications. --> Can be slower.

実行結果 Result of execution プロセス数を増やすと遅くなる！　 The program gets slow down as the number of processes increased. $ mpirun -np 8 ./mpi-2.exe Result: 2.582018e+02 number of processes: 8 Elapsed time: 2.067089e-03 sec. $ mpirun -np 2 ./mpi-2.exe Result: 2.565114e+02 number of processes: 2 Elapsed time: 5.409718e-04 sec. $ mpirun -np 1 ./mpi-2.exe Result: 2.539768e+02 number of processes: 1 Elapsed time: 1.161098e-04 sec. 今回のプログラムは計算量が少なすぎて 並列化の効果よりも通信時間の方が 長かった． 　ベクトルの内積：　O(N) 　行列同士の積：　Ｏ（Ｎ3） Amount of calculation in this program is too small. So, the effect of the parallelization is much smaller than the time for communication. Dot-product of vectors: O(N) Matrix-Matrix multiply: O(N3)

Today's Topic ノンブロッキング通信 Non-Blocking Communication 通信の完了を待つ間に他の処理を行う 　Execute other instructions while waiting for the completion of a communication. 集団通信関数の実装 Implementation of collective communications デッドロック Deadlock 　

ノンブロッキング通信関数 Non-blocking communication functions ノンブロッキング = ある命令の完了を待たずに次の命令に移る Non-blocking = Do not wait for the completion of an instruction and proceed to the next instruction Example) MPI_Irecv & MPI_Wait Blocking Non-Blocking MPI_Recv Proceed to the next instruction without waiting for the data MPI_Irecv next instructions Wait for the arrival of data data data MPI_Wait next instructions

MPI_Irecv Non-Blocking Receive request: 通信要求 Communication Request Usage: int MPI_Irecv(void *b, int c, MPI_Datatype d, int src, int t, MPI_Comm comm, MPI_Request *r); Non-Blocking Receive Parameters: start address for storing received data, number of elements, data type, rank of the source, tag (= 0, in most cases), communicator (= MPI_COMM_WORLD, in most cases), request request: 通信要求 Communication Request この通信の完了を待つ際に用いる Used for Waiting completion of this communication Example) MPI_Request req; ... MPI_Irecv(a, 100, MPI_INT, 0, 0, MPI_COMM_WORLD, &req); ... MPI_Wait(&req, &status); 7 7

MPI_Isend Non-Blocking Send Usage: int MPI_Send(void *b, int c, MPI_Datatype d, 　　　　　　　　　　　　　int dest, int t, MPI_Comm comm); Non-Blocking Send Parameters: start address for sending data, number of elements, data type, rank of the destination, tag (= 0, in most cases), communicator (= MPI_COMM_WORLD, in most cases), request Example) MPI_Request req; ... MPI_Isend(a, 100, MPI_INT, 1, 0, MPI_COMM_WORLD, &req); ... MPI_Wait(&req, &status); 8 8

Non-Blocking Send? Blocking send (MPI_Send): 送信データが別の場所にコピーされるのを待つ Wait for the data to be copied to somewhere else. ネットワークにデータを送出し終わるか、一時的にデータのコピーを作成するまで。 Until completion of the data to be transferred to the network or, until completion of the data to be copied to a temporal memory. Non-Blocking send (MPI_Recv): 待たない 　

Value of A at here can be 10 or 50 Notice: ノンブロッキング通信中はデータが不定 　Data is not sure in non-blocking communications MPI_Irecv: 受信データの格納場所と指定した変数の値は MPI_Waitまで不定 Value of the variable specified for receiving data is not fixed before MPI_Wait A arrived data MPI_Irecv to A 10 ... ~ = A A 50 Value of A at here can be 10 or 50 50 MPI_Wait Value of A is 10 ~ = A

Notice: ノンブロッキング通信中はデータが不定 　Data is not sure in non-blocking communications MPI_Isend: 送信データを格納した変数を MPI_Waitより前に書き換えると、実際に送信される値は不定 If the variable that stored the data to be sent is modified before MPI_Wait, the value to be actually sent is unpredictable. A MPI_Isend A Modifying value of A here causes incorrect communication 10 ... A = 50 data sent A 10 or 50 50 MPI_Wait You can modify value of A at here without any problem A = 100

MPI_Wait Usage: int MPI_Wait(MPI_Request *req, MPI_Status *stat); ノンブロッキング通信（MPI_Isend、 MPI_Irecv）の完了を待つ。 Wait for the completion of MPI_Isend or MPI_Irecv 送信データの書き換えや受信データの参照が行える Make sure that sending data can be modified, or receiving data can be referred. Parameters: request, status status: MPI_Irecv 完了時に受信データの statusを格納 The status of the received data is stored at the completion of MPI_Irecv

MPI_Waitall Usage: int MPI_Waitall(int c, MPI_Request *requests, MPI_Status *statuses); 指定した数のノンブロッキング通信の完了を待つ Wait for the completion of specified number of non-blocking communications Parameters: count, requests, statuses count: ノンブロッキング通信の数 The number of non-blocking communications requests, statuses: 少なくとも count個の要素を持つ MPI_Request と MPI_Statusの配列 Arrays of MPI_Request or MPI_Status that consists at least 'count' number of elements.

集団通信関数の中身 Inside of the functions of collective communications 通常，集団通信関数は， 　 MPI_Send, MPI_Recv, MPI_Isend, MPI_Irecv 等の一対一通信で実装される Usually, functions of collective communications are implemented by using message passing functions.

Inside of MPI_Bcast One of the most simple implementations int MPI_Bcast(char *a, int c, MPI_Datatype d, int root, MPI_Comm comm) { int i, myid, procs; MPI_Status st; MPI_Comm_rank(comm, &myid); MPI_Comm_rank(comm, &procs); if (myid == root){ for (i = 0; i < procs) if (i != root) MPI_Send(a, c, d, i, 0, comm); } else{ MPI_Recv(a, c, d, root, 0, comm, &st); } return 0; }

Another implementation: With MPI_Isend int MPI_Bcast(char *a, int c, MPI_Datatype d, int root, MPI_Comm comm) { int i, myid, procs; MPI_Status st, *stats; MPI_Request *reqs; MPI_Comm_rank(comm, &myid); MPI_Comm_rank(comm, &procs); if (myid == root){ stats = (MPI_Status *)malloc(sizeof(MPI_Status)*procs); reqs = (MPI_Request *)malloc(sizeof(MPI_Request)*procs); for (i = 0; i < procs) if (i != root) MPI_Isend(a, c, d, i, 0, comm); MPI_Waitall(procs, reqs, stats); free(stats); free(reqs); } else{ MPI_Recv(a, c, d, root, 0, comm, &st); } return 0; }

Another implementation: Binomial Tree int MPI_Bcast(char *a, int c, MPI_Datatype d, int root, MPI_Comm comm) { int i, myid, procs; MPI_Status st; int mask, relative_rank, src, dst; int tag = 1, success = 0; MPI_Comm_rank(comm, &myid); MPI_Comm_rank(comm, &procs); relative_rank = myid - root; if (relative_rank < 0) relative_rank += procs; mask = 1; while (mask < num_procs){ if (relative_rank & mask){ src = myid - mask; if (src < 0) src += procs; MPI_Recv(a, c, d, src, 0, comm, &st); break; } mask <<= 1; mask >>= 1; while (mask > 0){ if (relative_rank + mask < procs){ dst = myid + mask; if (dst >= procs) dst -= procs; MPI_Send (a, c, d, dst, 0, comm); } return 0;

Flow of Binomial Tree Use 'mask' to determine when and how to Send/Recv Rank 0 Rank 1 Rank 2 Rank 3 Rank 4 Rank 5 Rank 6 Rank 7 mask = 1 mask = 1 mask = 1 mask = 1 mask = 1 mask = 1 mask = 1 mask = 1 mask = 2 mask = 2 mask = 2 mask = 2 Recv from 6 Recv from 0 Recv from 2 Recv from 4 mask = 4 mask = 4 Recv from 0 Recv from 4 Recv from 0 mask = 4 Send to 4 mask = 2 Send to 6 mask = 2 mask = 1 Send to 2 mask = 1 Send to 5 Send to 7 mask = 1 Send to 3 mask = 1 Send to 1

Deadlock 何らかの理由で、プログラムを進行させることができなくなった状態 A status of a program in which it cannot proceed by some reasons. MPIプログラムでデッドロックが発生しやすい場所： Places you need to be careful for deadlocks: 1. MPI_Recv, MPI_Wait, MPI_Waitall 　　　　　 2. Collective communications 　全部のプロセスが同じ集団通信関数を実行するまで先に進めない A program cannot proceed until all processes call 　 the same collective communication function Wrong case: One solution: use MPI_Irecv if (myid == 0){ MPI_Recv from rank 1 MPI_Send to rank 1 } if (myid == 1){ MPI_Recv from rank 0 MPI_Send to rank 1 } if (myid == 0){ MPI_Irecv from rank 1 MPI_Send to rank 1 MPI_Wait } if (myid == 1){ MPI_Irecv from rank 0 MPI_Send to rank 0 MPI_Wait }

Summary 並列プログラムの作成には， 　計算の分割，データの分割，通信が必要 Parallel programs need distribution of computation, distribution of data and communications. 並列化で必ず高速化できるとは限らない Parallelization does not always speed up programs. 並列化出来ないプログラムがある There are non-parallelizable programs 並列プログラムではデッドロックに注意 Be careful about deadlocks.

Report) Make Reduce function by yourself 次のページのプログラムの my_reduce関数の中身を追加してプログラムを完成させる Fill the inside of 'my_reduce' function in the program shown in the next slide my_reduce: MPI_Reduceの簡略版 Simplified version of MPI_Reduce 整数の総和のみ. ルートランクは 0限定． コミュニケータは MPI_COMM_WORLD Calculates total sum of integer numbers. The root rank is always 0. The communicator is always MPI_COMM_WORLD. アルゴリズムは好きなものを考えてよい Any algorithm is OK.

complete here by yourself #include <stdio.h> #include <stdlib.h> #include "mpi.h" #define N 20 int my_reduce(int *a, int *b, int c) { return 0; } int main(int argc, char *argv[]) int i, myid, procs; int a[N], b[N]; MPI_Init(&argc, &argv); MPI_Comm_rank(MPI_COMM_WORLD, &myid); MPI_Comm_size(MPI_COMM_WORLD, &procs); for (i = 0; i < N; i++){ a[i] = i; b[i] = 0; my_reduce(a, b, N); if (myid == 0) for (i = 0; i < N; i++) printf("b[%d] = %d , correct answer = %d\n", i, b[i], i*procs); MPI_Finalize(); complete here by yourself