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In this section, we exemplify the use of TAMPI and NAM windows through the Heat benchmark. We use an iterative Gauss-Seidel method to solve the Heat equation, which is a parabolic partial differential equation that describes the distribution of heat in a given region over time. This benchmark simulates the heat diffusion on a 2D matrix of floating-point elements during multiple timesteps. The 2D matrix is logically divided into 2D blocks and may have multiple rows and columns of blocks. The computation of an element at position M[r][c] in the timestep t depends on the value of the top and left elements (M[r-1][c] and M[r][c-1]) computed in the current timestep t, and the right and bottom elements (M[r][c+1] and M[r+1][c]) from the previous timestep t-1. We can extrapolate this logic in the context of blocks so that a block has a dependency on the computation of its adjacent blocks. Notice that the computation of blocks in a diagonal is fully concurrent because there is no dependency between them.
There are three different MPI versions, and all of them distribute the 2D matrix across ranks assigning consecutive rows of blocks to each MPI rank. Note that the matrix is distributed by blocks vertically but not horizontally. Therefore, an MPI rank has two neighboring ranks: one above and another below. The exceptions are the first and last ranks since they have a single neighbor. This distribution requires the neighboring ranks to exchange the external rows (halos) from their boundary blocks in order to compute their local blocks in each timestep.
This benchmark is publicly available in the ?https://pm.bsc.es/gitlab/DEEP-EST/apps/Heat repository. The first version is based on an MPI-only parallelization, while the other two are hybrid MPI+OmpSs-2 leveraging tasks and the TAMPI library. We briefly describe each one below:
01.heat_mpi.bin: A straightforward MPI-only implementation using blocking MPI primitives (MPI_Send and MPI_Recv) to send and receive the halo rows. The computation of blocks and exchange of halos inside each rank is completely sequential.
02.heat_itampi_ompss2_tasks.bin: A hybrid MPI+OmpSs-2 version leveraging TAMPI that performs both computation and communications using tasks with data dependencies. It instantiates a task to compute each of the blocks inside each rank and for each of the timesteps. It also creates a sending and receiving tasks to exchange the block halo rows for each of the boundary blocks. The execution of tasks follows a data-flow model because tasks declare the dependencies on the data they read/modify. Moreover, communication tasks call non-blocking MPI primitives and leverage the non-blocking mechanism of TAMPI (TAMPI_Iwait), so communications are fully non-blocking and asynchronous from the user point of view. Communication tasks issue non-blocking communications that are transparently managed and periodically checked by TAMPI. These tasks do not explicitly wait for their communication, but they delay their completion (asynchronously) until their MPI communications finish.
03.heat_tampirma_ompss2_tasks.bin: An implementation similar to 02.heat_itampi_ompss2_tasks.bin but using MPI RMA operations (MPI_Put) to exchange the block halo rows. This program leverages the MPI active target RMA communication using the MPI window fences to open/close RMA access epochs. It uses the TAMPI library and the new integration for the MPI_Win_ifence synchronization function. In this way, we use TAMPI_Iwait to bind the completion of a communication task to the finalization of a MPI_Win_ifence. Therefore, the opening/closing of RMA access epochs is completely non-blocking and asynchronous from the user point of view. We assume the calls to MPI_Put are non-blocking. Finally, as an optimization, we register multiple MPI RMA windows for each rank to allow concurrent communications through the different RMA windows. Each RMA window holds a part of the halo row that may belong to multiple logical blocks. Each communication task exchanges the part of the halo row assigned to a single MPI window.
The requirements of this application are shown in the following lists. The main requirements are:
In this benchmark, we use the NAM memory to perform checkpointing of the matrix that we are computing. During the execution of the application and every a few timesteps, the benchmark instantiate multiple tasks that save the whole matrix into a NAM region. There is a task for saving the data of each block into that region and may run in parallel.
The instructions to build and execute the Heat benchmark with NAM checkpointing will appear here soon.