1 / 39

Parallel Processing (CS 676) Lecture: Grouping Data and Communicators in MPI

Parallel Processing (CS 676) Lecture: Grouping Data and Communicators in MPI. Jeremy R. Johnson *Parts of this lecture was derived from chapters 6,7 in Pacheco. Introduction.

collin
Download Presentation

Parallel Processing (CS 676) Lecture: Grouping Data and Communicators in MPI

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Parallel Processing (CS 676)Lecture: Grouping Data and Communicators in MPI Jeremy R. Johnson *Parts of this lecture was derived from chapters 6,7 in Pacheco Parallel Processing

  2. Introduction • Objective: To introduce MPI commands for creating types and communicators. To discuss performance models and considerations in MPI and ways of reducing communication. • Topics • MPI Datatypes and packing • Revised version of Get_Data • Matrix transposition • Creating communicators • Topologies • Grids • Matrix Multiplication • Fox’s algorithm • Performance Model Parallel Processing

  3. Derived Types • Due to latency of communication it is usually a good idea to package up several elements into a single message • MPI_Send and MPI_Recv, allow message to be given by a start address, basic type, and a count. • This allows multiple data elements to be sent in one message • Requires elements to be of the same type • Must be contiguous • A generalized type • {(t0,d0),…,(tn-1,dn-1)} • ti is an existing type • di is a displacement Parallel Processing

  4. Functions for Creating MPI Types • int MPI_Type_struct(int count, int block_lengths[], MPI_Aint displacements[], MPI_Datatype typelist[], MPI_Datatype new_mpi_t) • MPI_Address( void* location, MPI_Aint* address) • int MPI_Type_commit(MPI_Datatype* new_mpi_t) Parallel Processing

  5. Other Derived Datatype Constructors • int MPI_Type_vector(int count, int block_length, int stride, MPI_Datatype element_type, MPI_Datatype new_mpi_t) • int MPI_Type_contiguous(int count, MPI_Datatype old_type, MPI_Datatype new_mpi_t) • int MPI_Type_indexed(int count, int block_lengths[], int displacements[], MPI_Datatype old_type, MPI_Datatype new_mpi_t) Parallel Processing

  6. Transpose float A[10][10]; /* stored in row-major order. */ /* Send 3rd row of A from process 0 to process 1. */ If (my_rank == 0) { MPI_Send(&(A[2][0]), 10, MPI_FLOAT, 1, 0, MPI_COMM_WORLD); } else { MPI_Recv(&(A[2][0]), 10, MPI_FLOAT, 0, 0, MPI_COMM_WORLD, &status); } /* Doesn’t work for columns, since not contiguous. */ Parallel Processing

  7. Transpose float A[10][10]; /* stored in row-major order. */ /* Send 3rd column of A from process 0 to process 1. */ MPI_Type_vector(10, 1, 10, MPI_FLOAT, &column_mpi_t); MPI_Type_commit(&column_mpi_t); If (my_rank == 0) { MPI_Send(&(A[0][2]), 1, column_mpi_t, 1, 0, MPI_COMM_WORLD); } else { MPI_Recv(&(A[0][2]), 1, column_mpi_t, 0, 0, MPI_COMM_WORLD, &status); } Parallel Processing

  8. Upper Triangular Matrix float A[n][n]; /* Complete matrix */ float T[n][n]; /* Upper triangle. */ int displacements[n]; int block_lengths[n]; MPI_Datatype index_mpi_t; for(i = 0; i < n; i++) { block_lengths[i] = n-i; displacements[i] = (n+1)*i; } MPI_Type_indexed(n, block_lengths, displacments, MPI_FLOAT, &index_mpi_t); MPI_Type_commit(&index_mpi_t); if (my_rank == 0) { MPI_Send(A, 1, index_mpi_t, 1, 0, MPI_COMM_WORLD); else MPI_Recv(T, 1, index_mpi_t, 0, 0, MPI_COMM_WORLD, &status); Parallel Processing

  9. Type Matching • When can a receiving process match the data sent by a sending process? • MPI_Send(message, send_count, send_mpi_t, 1, 0, MPI_COMM_WORLD) • MPI_Recv(message, recv_count, recv_mpi_t, 0, 0,MPI_COMM_WORLD,&status) • Given a derived type {(t0,d0),…,(tn-1,dn-1)} • Displacements do not matter • Type signatures {t0,…,tn-1} and {u0,…,um-1} must be compatible • n  m, ti =ui for i=0,…,n-1 • For collective communications sending and receiving types must be identical Parallel Processing

  10. Type Matching Example • For type column_mpi_t (column of 10  10 array of floats) • {(MPI_FLOAT,0), (MPI_FLOAT,10*sizeof(float)), • (MPI_FLOAT,20*sizeof(float)),…,(MPI_FLOAT,90*sizeof(float))} • Signature is {MPI_FLOAT,…,MPI_FLOAT}, MPI_FLOAT 10 times • Example: Can send column to row float A[10][10]; /* stored in row-major order. */ If (my_rank == 0) MPI_Send(&(A[0][0]), 1, column_mpi_t, 1, 0, MPI_COMM_WORLD); else if (my_rank == 0) MPI_Recv(&(A[0][0]),10, MPI_FLOAT, 0, 0, MPI_COMM_WORLD, &status); Parallel Processing

  11. Pack and Unpack • MPI_Pack and MPI_Unpack allow a user to copy non-contiguous memory locations into a contiguous buffer and to copy a contiguous buffer into non-contiguous memory locations • int MPI_Pack(void* pack_data, int in_count, MPI_Datatype datatype, void* buffer, int buffer_size, int* position, MPI_Comm comm) • On input copy data starting at location &buffer + position • On output position points to first location in the buffer after pack_data • int MPI_Unpack(void* buffer, int size, int* position,void* unpack_data, int count,MPI_Datatype datatype, MPI_Comm comm) • Data starting at location &buffer + *position is copied into memory referenced by unpack_data • count data elements of type datatype are copied into unpack_data • position is updated to point to location in buffer after the data just copied • Messages constructed with MPI_Pack should be communicated with datatype argument MPI_PACKED Parallel Processing

  12. Deciding which Method to Use • Creating a derived type has overhead associated with it. • Depends on number of times type will be used. • Can avoid system buffering with Pack/Unpack • Can use variable length messages with Pack/Unpack Parallel Processing

  13. Variable Length Messages float* entries; int* column_subscripts; int nonzeros; int position; int row_number; char buffer[HUGE]; if (my_rank == 0) { position = 0; MPI_Pack(&nonzeros,1,MPI_INT,buffer,HUGE,&position,MPI_COMM_WORLD); MPI_Pack(row_number,1,MPI_INT,buffer,HUGE,&position,MPI_COMM_WORLD); MPI_Pack(entries,nonzeros,MPI_FLOAT,buffer,HUGE, &position,MPI_COMM_WORLD); MPI_Pack(column_subscripts,nonzeros,MPI_INT,buffer,HUGE, &position,MPI_COMM_WORLD); MPI_Send(buffer,position,MPI_PACKED, 1,0,MPI_COMM_WORLD); } Parallel Processing

  14. Variable Length Messages (cont) else { MPI_Recv(buffer,HUGE,MPI_PACKED, 0,0, MPI_COMM_WORLD, &status); position = 0; MPI_UnPack(buffer,HUGE,&position, &nonzeros, MPI_INT,MPI_COMM_WORLD); MPI_UnPack(buffer,HUGE,&position, &row_number, MPI_INT, MPI_COMM_WORLD); entries = (float *) malloc(nonzeros*sizeof(float)); column_subscripts = (int *) malloc(nonzeros*sizeof(int)); MPI_UnPack(buffer,HUGE,&position, entries, MPI_FLOAT,nonzeros, MPI_COMM_WORLD); MPI_UnPack(buffer,HUGE,&position, &column_subscripts, MPI_INT, nonzeros, MPI_COMM_WORLD); } Parallel Processing

  15. Communicators • A mechanism to treat a subset of processes as a universe for communication (both point-to-point and collective) • Types • intra-communicator • inter-communicator • Components • group (ordered collection of processes) • context (unique identifier) • optional additional information such as topology • Create new communicators from existing communicators Parallel Processing

  16. Working with Groups, Contexts, and Communicators • MPI_Comm_group(MPI_Comm comm, MPI_Group* group) • MPI_Group_incl(MPI_Group old_group, int new_group_size, int ranks_in_old_group[]; MPI_Group* new_group) • MPI_Comm_create(MPI_Comm old_comm, MPI_Group group, MPI_Comm* new_com) Parallel Processing

  17. Creating a Communicator /* Create communicator out of first row of q^2 processes organized in a q  q grid in row-major order. */ MPI_Group group_world; MPI_Group first_row_group; MPI_Comm first_row_comm; int* process_ranks; process_ranks = (int*) malloc(q*sizeof(int)); for (proc = 0; proc < q; proc++) process_ranks[proc] = proc; MPI_Comm_Group(MPI_COMM_WORLD,&group_world); MPI_Group_incl(group_world,q,process_ranks,&first_row_group); MPI_Comm_create(MPI_COMM_WORLD,first_row_group,&first_row_comm); Parallel Processing

  18. Using a Communicator /* Broadcast first block to all processes in the same row. */ int my_rank_in_first_row; float* A00; if (my_rank < q) { MPI_Comm_rank(first_row_comm,&my_rank_in_first_row); A_00 = (float *) malloc(n_bar*n_bar*sizeof(float)); if (my_rank_in_first_row == 0) { /* initialize A_00 */} MPI_Bcast(A_00,n_bar*n_bar,MPI_FLOAT,0,first_row_comm); } Parallel Processing

  19. MPI_Comm_split • int MPI_Comm_split(MPI_Comm old_comm, int split_key, int rank_key, MPI_Comm new_comm) MPI_Comm my_row_comm; int my_row; /* my_rank is in MPI_COMM_WORLD, q*q = p */ my_row = my_rank/q; MPI_Comm_split(MPI_COMM_WORLD,my_row,my_rank,&my_row_comm); /* Creates q new communicators. Processes with the same value of split_key form a new group. The rank in the new communicator is determined by rank_key. Order is preserved. If the same rank_key is used, then the choice is arbitrary. */ Parallel Processing

  20. Topologies • Communicators can have attributes. One such attribute is a topology. • A topology is a mechanism for associating a different addressing scheme with processes belonging to a group. • Provides a virtual interconnection organization of processes that may be convenient for a particular algorithm. • Types • Cartesian (grid) • Graph Parallel Processing

  21. Working with Cartesian Topologies • MPI_Cart_create(MPI_Comm old_comm, int number_of_dims, int dim_sizes[], int wrap_around[], int reorder, MPI_Comm* cart_comm) • MPI_Cart_rank(MPI_Comm comm, int rank, int number_of_dims, int* rank) • MPI_Cart_coords(MPI_Comm comm, int rank, int number_of_dims, int coordinates[]) • MPI_Cart_sub(MPI_Comm cart_comm, int free_coords[], MPI_Comm* new_comm) Parallel Processing

  22. Creating a Cartesian Topology /* create communicator with 2D grid topology. */ MPI_Comm grid_comm; int dim_sizes[2]; int wrap_around[2]; int reorder = 1; dim_sizes[0] = dim_sizes[1] = q; wrap_around[0] = wrap_around[1] = 1; MPI_Cart_create(MPI_COMM_WORLD, 2, dim_sizes,wrap_around,reorder, &grid_comm); Parallel Processing

  23. Creating a Sub-Cartesian Topology int free_coords[2]; MPI_Comm row_comm; /* create communicator for each row of grid_comm */ free_coords[0] = 0; free_coords[1] = 1; MPI_Cart_sub(grid_comm, free_coords, &row_comm) /* create communicator for each column of grid_comm */ free_coords[0] = 1; free_coords[1] = 0; MPI_Cart_sub(grid_comm, free_coords, &col_comm) Parallel Processing

  24. Cartesian Addressing int coordinates[2]; int my_grid_rank; MPI_Comm_rank(grid_comm, &my_grid_rank); MPI_Cart_coords(grid_comm, my_grid_rank,2, coordinates); /* inverse operation */ MPI_Cart_rank(grid_comm, coordinates, &my_grid_rank) Parallel Processing

  25. Matrix Multiplication • Let A, B be n  n matrices, and C = A*B void Serial_matrix_mult(MATRIX_T A, MATRIX_T B, MATRIX_T C, int n) { int i,j,k; for (i=0; i< n; i++) for (j=0; j< n;j++) { C[i][j] = 0.0; for (k=0; k < n;k++) C[i][j] = C[i][j] + A[i][k]*B[k][j]; } } Parallel Processing

  26. Parallel Matrix Multiplication /* distribute matrices by rows. */ void Parallel_matrix_mult(MATRIX_T A, MATRIX_T B, MATRIX_T C, int n) { for each column of B { Allgather(column); Compute dot product of my row of A with column; } /* can distribute matrices by blocks of rows. Also B could be distributed by * columns */ Parallel Processing

  27. Cyclic Matrix Multiplication /* Arrange processors in a circle, storing rows of A and B in each process. Ci.* = Ai,0 * B0,* + … + Ai,n-1 * Bn-1,* */ void Parallel_matrix_mult(MATRIX_T A, MATRIX_T B, MATRIX_T C, int n) { i = rank; Blocal = ith row of B; Alocal = ith row of A; Clocal = 0; /* ith row of C */ dest = (i+1) % n; src = (i-1) % n; for (k=0;k<n;k++) { Ci,* = Ci,* + Ai,i+kmod n* Bi+k mod n,* send_recv(Blocal,dest,src); } Parallel Processing

  28. Fox’s Matrix Multiplication • Let A, B be p  p matrices, and C = A*B • Organize processors into a q  q grid, q = sqrt(p) • Store (i,j) block on processor (i,j) • Broadcast elements of A as k = 0,…,q-1 • Cyclically rotate elements of B. Parallel Processing

  29. Example Parallel Processing

  30. Fox’s Matrix Multiplication /* Uses a block matrix allocation. Group processors in a q × q grid, where q = sqrt(p). Processor (i,j) stores Aij and initially Bij */ void Parallel_matrix_mult(MATRIX_T A, MATRIX_T B, MATRIX_T C, int n) { i = my process row; j = my process column; dest = ((i-1) % q,j); src = ((i+1) % q,j); for (stage=0;stage < q; stage++) { k_bar = (i + stage) mod q; Broadcast A[i,k_bar] across process row i; C[i,j] = C[i,j] + A[i,k_bar]*B[k_bar,j]; Send B[k_bar,j] to dest; Receive B[(k_bar+1) mod q,j] from source; } Parallel Processing

  31. Variant of Fox’s Matrix Multiplication • Let A, B be q  q matrices, and C = A*B • Organize processors into a sqrt(p)  sqrt(p) grid • Store (i,j+i mod q) block of A and (i+j mod q,j) block of B on processor (i,j) • Cyclically rotate rows of A to the left. • Cyclically rotate columns of B upward. Parallel Processing

  32. Example Parallel Processing

  33. Variant of Fox’s Matrix Multiplication /* Uses a block matrix allocation. Group processors in a q × q grid, where q = sqrt(p). Processor (i,j) stores Ai,i+j and initially Bi+i,j */ void Parallel_matrix_mult(MATRIX_T A, MATRIX_T B, MATRIX_T C, int n) { i = my process row; j = my process column; coldest = ((i-1) % q,j); colsrc = ((i+1) % q,j); rowdest = (i,(j-1) % q); rowsrc = (i,(j+1) % q); for (stage=0;stage < q; stage++) { k_bar = (i +j + stage) mod q; C[i,j] = C[i,j] + A[i,k_bar]*B[k_bar,j]; Send_Recv A[i,k_bar] to/from rowdest,rowsrc; Send_Recv B[k_bar,j] to/from coldest, colsrc; } Parallel Processing

  34. Performance Model • Communication cost: C(n) = +n •  = latency • 1/ = bandwidth • Empirically determine  and  by measuring time to send/recv messages with different lengths • Least squares fit Parallel Processing

  35. Analysis of Matrix Multiplication • Let A, B be n  n matrices, and C = A*B • Sequential cost • T(n)= an3+bn2+cn+d = (n3) • Least squares fit • T(n)  an3 Parallel Processing

  36. Analysis of Parallel Matrix Multiplication (Allgather) • Let A, B be n  n matrices, and C = A*B • Let p = number of processors • Store ith block of n/p rows of A, B, and C on process i • Parallel computing time: (n3/p + plog(p) + n2log(p)) • Computation time: p(n/p  n  n/p) = n3/p • Communication time: p(log(p)(+n2/p) [Allgather] Parallel Processing

  37. Analysis of Parallel Matrix Multiplication (Cyclic) • Let A, B be n  n matrices, and C = A*B • Let p = number of processors • Store ith block of n/p rows of A, B, and C on process i • Parallel computing time: (n3/p + p + n2) • Computation time: p(n/p  n/p  n ) = n3/p • Communication time: p(+n2/p) Parallel Processing

  38. Analysis of Parallel Matrix Multiplication (Fox) • Let A, B be n  n matrices, and C = A*B • Let p = q2 number of processors organized in a q  q grid • Store (i,j)th n/q  n/q block of A, B, and C on process (i,j) • Parallel computing time: • (n3/p + qlog(q) + log(q)n2/q) • Computation time: q(n/q  n/q  n/q ) = n3/q2 = n3/p • Communication time: qlog(q)(+(n/q)2) Parallel Processing

  39. Analysis of Parallel Matrix Multiplication (Fox Variant) • Let A, B be n  n matrices, and C = A*B • Let p = q2 number of processors organized in a q  q grid • Store (i,j)th n/q  n/q block of A, B, and C on process (i,j) • Parallel computing time: • (n3/p + q + n2/q) • Computation time: q(n/q  n/q  n/q ) = n3/q2 = n3/p • Communication time: q(+(n/q)2) Parallel Processing

More Related