/* * Returns flops per cycle. */ double time_mult(long dim, enum mult_flag_enum flag){ int count = 10; double *a = new double[dim*dim]; double *b = new double[dim*dim]; double *c = new double[dim*dim]; #pragma omp parallel for for(long i=0; i < dim*dim; i++) a[i] = b[i] = c[i] = 1; TimeStamp clk; StatVector stats(count); if(flag == AUTO) mkl_mic_enable(); for(int i=0; i < count; i++){ clk.tic(); switch(flag){ case HOST: mmult(a, b, c, dim); break; case MIC: #pragma offload target(mic) \ in(a:length(dim*dim) align(64) alloc_if(1) free_if(1)) \ in(b:length(dim*dim) align(64) alloc_if(1) free_if(1)) \ inout(c: length(dim*dim) align(64) alloc_if(1) free_if(1)) mmult(a, b, c, dim); break; case AUTO: mmult(a, b, c, dim); break; } double cycles = clk.toc(); stats.insert(cycles); } if(flag == AUTO) mkl_mic_disable(); delete[] a; delete[] b; delete[] c; return 2.0*dim*dim*dim/stats.median(); }
void cholesky_tiled(double *mat, int tile_size, int num_tiles, int mat_size, int niter, int max_log_str, bool layRow, int verify) { //total number of tiles int tot_tiles = num_tiles * num_tiles; //memory allocation for matrix for tiled-Cholesky double *A_my = (double *)malloc(mat_size * mat_size * sizeof(double)); //memory allocation for matrix for MKL cholesky (for comparison) double *A_MKL = (double *)malloc(mat_size * mat_size * sizeof(double)); //memory allocation for tiled matrix double **Asplit = new double* [tot_tiles]; int mem_size_tile = tile_size * tile_size * sizeof(double); for (int i = 0; i < tot_tiles; ++i) { //Buffer per tile, host allocation Asplit[i] = (double *)_mm_malloc(mem_size_tile, 64); //Buffer creation and allocation on the card hStreams_app_create_buf((void *)Asplit[i], mem_size_tile); } double tbegin, tend; int iter; int info; //Events are needed for various synchronizations to enforce //data dependence between and among data-transfers/computes HSTR_EVENT *eventcpyto = new HSTR_EVENT[tot_tiles]; HSTR_EVENT *eventcpyfr = new HSTR_EVENT[tot_tiles]; HSTR_EVENT *eventpotrf = new HSTR_EVENT[tot_tiles]; HSTR_EVENT *eventtrsm = new HSTR_EVENT[tot_tiles]; HSTR_EVENT *eventsyrk = new HSTR_EVENT[tot_tiles]; HSTR_EVENT *eventgemm = new HSTR_EVENT[tot_tiles]; //for timing tiled cholesky double *totTimeMsec = new double [niter]; //for timing MKL cholesky double *totTimeMsecMKL = new double [niter]; HSTR_RESULT res; //these queues are used for queining up compute on the card and //data transfers to/from the card. //q_trsm for dtrsm, q_potrf for dportf, q_syrk_gemm for both dsyrk and dgemm. //The queues are incremented by one for every compute queued and wrap //around the max_log_str available. This ensures good load-balancing. int q_trsm, q_potrf, q_syrk_gemm; CBLAS_ORDER blasLay; int lapackLay; if (layRow) { blasLay = CblasRowMajor; lapackLay = LAPACK_ROW_MAJOR; } else { blasLay = CblasColMajor; lapackLay = LAPACK_COL_MAJOR; } for (iter = 0; iter < niter; ++iter) { //copying matrices into separate variables for tiled cholesky (A_my) //and MKL cholesky (A_MKL) //The output overwrites the matrices and hence the need to copy //for each iteration copy_mat(mat, A_my, mat_size); copy_mat(mat, A_MKL, mat_size); unsigned int m, n, k; printf("\nIteration = %d\n", iter); split_into_blocks(A_my, Asplit, num_tiles, tile_size, mat_size, layRow); //beginning of timing tbegin = dtimeGet(); //splitting time included in the timing //This splits the input matrix into tiles (or blocks) //split_into_blocks(A_my, Asplit, num_tiles, tile_size, mat_size, layRow); q_potrf = 0; for (k = 0; k < num_tiles; ++k) { //POTRF //dpotrf is executed on the host on the diagonal tile //the results are then sent to the card if (k > 0) { hStreams_app_event_wait(1, &eventsyrk[k * num_tiles + k]); if (loc_verbose > 0) printf("Sending tile[%d][%d] to host in queue %d\n", k, k, (int)(q_potrf % max_log_str)) ; hStreams_app_xfer_memory(Asplit[k * num_tiles + k], Asplit[k * num_tiles + k], mem_size_tile, (int)(q_potrf % max_log_str), HSTR_SINK_TO_SRC, &eventcpyfr[k * num_tiles + k]); hStreams_app_event_wait(1, &eventcpyfr[k * num_tiles + k]); } if (loc_verbose > 0) { printf("Executing potrf on host for tile[%d][%d]\n", k, k); } info = LAPACKE_dpotrf(lapackLay, 'L', tile_size, Asplit[k * num_tiles + k], tile_size); if (k < num_tiles - 1) { if (loc_verbose > 0) printf("Sending tile[%d][%d] to card in queue %d\n", k, k, (int)(q_potrf % max_log_str)); hStreams_app_xfer_memory(Asplit[k * num_tiles + k], Asplit[k * num_tiles + k], mem_size_tile, (int)(q_potrf % max_log_str), HSTR_SRC_TO_SINK, &eventcpyto[k * num_tiles + k]); } q_potrf++; q_trsm = 0; for (m = k + 1; m < num_tiles; ++m) { if (k == 0) { if (loc_verbose > 0) printf("Sending tile[%d][%d] to card in queue %d\n", m, k, (int)(q_trsm % max_log_str)); hStreams_app_xfer_memory(Asplit[m * num_tiles + k], Asplit[m * num_tiles + k], mem_size_tile, (int)(q_trsm % max_log_str), HSTR_SRC_TO_SINK, &eventcpyto[m * num_tiles + k]); } //DTRSM hStreams_app_event_wait(1, &eventcpyto[k * num_tiles + k]); if (k > 0) { hStreams_app_event_wait(1, &eventgemm[m * num_tiles + k]); } //dtrsm is executed on the card if (loc_verbose > 0) printf("Executing trsm for tile[%d][%d] on card in queue %d\n", m, k, (int)(q_trsm % max_log_str)); res = hStreams_custom_dtrsm(blasLay, CblasRight, CblasLower, CblasTrans, CblasNonUnit, tile_size, tile_size, 1.0, Asplit[k * num_tiles + k], tile_size, Asplit[m * num_tiles + k], tile_size, (int)(q_trsm % max_log_str), &eventtrsm[m * num_tiles + k]); if (loc_verbose > 0) printf("Sending tile[%d][%d] back to host in queue %d\n", m, k, (int)(q_trsm % max_log_str)); hStreams_app_xfer_memory(Asplit[m * num_tiles + k], Asplit[m * num_tiles + k], mem_size_tile, (int)(q_trsm % max_log_str), HSTR_SINK_TO_SRC, &eventcpyfr[m * num_tiles + k]); q_trsm++; } q_syrk_gemm = 0; for (n = k + 1; n < num_tiles; ++n) { if (k == 0) { if (loc_verbose > 0) printf("Sending tile[%d][%d] to card in queue %d\n", n, n, (int)(q_syrk_gemm % max_log_str)); hStreams_app_xfer_memory(Asplit[n * num_tiles + n], Asplit[n * num_tiles + n], mem_size_tile, (int)(q_syrk_gemm % max_log_str), HSTR_SRC_TO_SINK, &eventcpyto[n * num_tiles + n]); } //DSYRK hStreams_app_event_wait(1, &eventtrsm[n * num_tiles + k]); if (k > 0) { hStreams_app_event_wait(1, &eventsyrk[n * num_tiles + n]); } //dsyrk is executed on the card if (loc_verbose > 0) printf("Executing syrk for tile[%d][%d] on card in queue %d\n", n, n, (int)(q_syrk_gemm % max_log_str)); res = hStreams_custom_dsyrk(blasLay, CblasLower, CblasNoTrans, tile_size, tile_size, -1.0, Asplit[n * num_tiles + k], tile_size, 1.0, Asplit[n * num_tiles + n], tile_size, (int)(q_syrk_gemm % max_log_str), &eventsyrk[n * num_tiles + n]); q_syrk_gemm++; for (m = n + 1; m < num_tiles; ++m) { if (k == 0) { if (loc_verbose > 0) printf("Sending tile[%d][%d] to card in queue %d\n", m, n, (int)(q_syrk_gemm % max_log_str)); hStreams_app_xfer_memory(Asplit[m * num_tiles + n], Asplit[m * num_tiles + n], mem_size_tile, (int)(q_syrk_gemm % max_log_str), HSTR_SRC_TO_SINK, &eventcpyto[m * num_tiles + n]); } //DGEMM hStreams_app_event_wait(1, &eventtrsm[m * num_tiles + k]); hStreams_app_event_wait(1, &eventtrsm[n * num_tiles + k]); if (k > 0) { hStreams_app_event_wait(1, &eventgemm[m * num_tiles + n]); } //dgemm is executed on the card if (loc_verbose > 0) printf("Executing gemm for tile[%d][%d] on card in queue %d\n", m, n, (int)(q_syrk_gemm % max_log_str)); res = hStreams_app_dgemm(blasLay, CblasNoTrans, CblasTrans, tile_size, tile_size, tile_size, -1.0, Asplit[m * num_tiles + k], tile_size, Asplit[n * num_tiles + k], tile_size, 1.0, Asplit[m * num_tiles + n], tile_size, (int)(q_syrk_gemm % max_log_str), &eventgemm[m * num_tiles + n]); q_syrk_gemm++; } } } //syncrhonizing all the streams hStreams_app_thread_sync(); //end of timing tend = dtimeGet(); totTimeMsec[iter] = 1e3 * (tend - tbegin); printf("time for Tiled hstreams Cholesky for iteration %d = %.2f msec\n", iter, totTimeMsec[iter]); //assembling of tiles back into full matrix assemble(Asplit, A_my, num_tiles, tile_size, mat_size, layRow); //calling mkl cholesky for verification and timing comparison. //Using auto-offload feature of MKL #ifndef _WIN32 //FIXME: calling this function causes a crash on Windows mkl_mic_enable(); #endif tbegin = dtimeGet(); //calling MKL dpotrf on the full matrix info = LAPACKE_dpotrf(lapackLay, 'L', mat_size, A_MKL, mat_size); tend = dtimeGet(); totTimeMsecMKL[iter] = 1e3 * (tend - tbegin); printf("time for MKL Cholesky (AO) for iteration %d = %.2f msec\n", iter, totTimeMsecMKL[iter]); if (info != 0) { printf("error with dpotrf\n"); } mkl_mic_disable(); if (verify == 1) { bool result = verify_results(A_my, A_MKL, mat_size * mat_size); if (result == true) { printf("Tiled Cholesky successful\n"); } else { printf("Tiled Chloesky failed\n"); } } } double meanTimeMsec, stdDevMsec; double meanTimeMsecMKL, stdDevMsecMKL; mean_and_stdev(totTimeMsec, meanTimeMsec, stdDevMsec, niter); mean_and_stdev(totTimeMsecMKL, meanTimeMsecMKL, stdDevMsecMKL, niter); double gflops = pow(mat_size, 3.0) / 3.0 * 1e-9; printf("\nMatrix size = %d\n", mat_size); printf("Tiled hStreams Cholesky: for %d iterations (ignoring first),\n" "mean Time = %.2f msec, stdDev Time = %.2f msec,\n" "Mean Gflops (using mean Time) = %.2f\n", niter - 1, meanTimeMsec, stdDevMsec, gflops / (meanTimeMsec * 1e-3)); printf("\nMKL AO Cholesky: for %d iterations (ignoring first),\n" "mean Time = %.2f msec, stdDev Time = %.2f msec,\n" "Mean Gflops (using meanTime) = %.2f\n\n", niter - 1, meanTimeMsecMKL, stdDevMsecMKL, gflops / (meanTimeMsecMKL * 1e-3)); //Free free(A_my); free(A_MKL); for (int i = 0; i < tot_tiles; ++i) { _mm_free(Asplit[i]); } delete [] Asplit; delete [] eventcpyto; delete [] eventcpyfr; delete [] eventpotrf; delete [] eventtrsm; delete [] eventsyrk; delete [] eventgemm; delete [] totTimeMsec; delete [] totTimeMsecMKL; }