FFTW 3.3.8: Basic and advanced distribution interfaces

As with the planner interface, the ‘fftw_mpi_local_size’ cannam@167: distribution interface is broken into basic and advanced cannam@167: (‘_many’) interfaces, where the latter allows you to specify the cannam@167: block size manually and also to request block sizes when computing cannam@167: multiple transforms simultaneously. These functions are documented cannam@167: more exhaustively by the FFTW MPI Reference, but we summarize the cannam@167: basic ideas here using a couple of two-dimensional examples. cannam@167:

For the 100 × 200 cannam@167: complex-DFT example, above, we would find cannam@167: the distribution by calling the following function in the basic cannam@167: interface: cannam@167:

cannam@167:

ptrdiff_t fftw_mpi_local_size_2d(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@167:                                  ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@167:

Given the total size of the data to be transformed (here,

n0 =
cannam@167: 100

and n1 = 200) and an MPI communicator (comm), this cannam@167: function provides three numbers. cannam@167:

First, it describes the shape of the local data: the current process cannam@167: should store a local_n0 by n1 slice of the overall cannam@167: dataset, in row-major order (n1 dimension contiguous), starting cannam@167: at index local_0_start. That is, if the total dataset is cannam@167: viewed as a n0 by n1 matrix, the current process should cannam@167: store the rows local_0_start to cannam@167: local_0_start+local_n0-1. Obviously, if you are running with cannam@167: only a single MPI process, that process will store the entire array: cannam@167: local_0_start will be zero and local_n0 will be cannam@167: n0. See Row-major Format. cannam@167: cannam@167:

Second, the return value is the total number of data elements (e.g., cannam@167: complex numbers for a complex DFT) that should be allocated for the cannam@167: input and output arrays on the current process (ideally with cannam@167: fftw_malloc or an ‘fftw_alloc’ function, to ensure optimal cannam@167: alignment). It might seem that this should always be equal to cannam@167: local_n0 * n1, but this is not the case. FFTW’s cannam@167: distributed FFT algorithms require data redistributions at cannam@167: intermediate stages of the transform, and in some circumstances this cannam@167: may require slightly larger local storage. This is discussed in more cannam@167: detail below, under Load balancing. cannam@167: cannam@167: cannam@167:

The advanced-interface ‘local_size’ function for multidimensional cannam@167: transforms returns the same three things (local_n0, cannam@167: local_0_start, and the total number of elements to allocate), cannam@167: but takes more inputs: cannam@167:

cannam@167:

ptrdiff_t fftw_mpi_local_size_many(int rnk, const ptrdiff_t *n,
cannam@167:                                    ptrdiff_t howmany,
cannam@167:                                    ptrdiff_t block0,
cannam@167:                                    MPI_Comm comm,
cannam@167:                                    ptrdiff_t *local_n0,
cannam@167:                                    ptrdiff_t *local_0_start);
cannam@167:

The two-dimensional case above corresponds to rnk = 2 and an cannam@167: array n of length 2 with n[0] = n0 and n[1] = n1. cannam@167: This routine is for any rnk > 1; one-dimensional transforms cannam@167: have their own interface because they work slightly differently, as cannam@167: discussed below. cannam@167:

First, the advanced interface allows you to perform multiple cannam@167: transforms at once, of interleaved data, as specified by the cannam@167: howmany parameter. (hoamany is 1 for a single cannam@167: transform.) cannam@167:

Second, here you can specify your desired block size in the n0 cannam@167: dimension, block0. To use FFTW’s default block size, pass cannam@167: FFTW_MPI_DEFAULT_BLOCK (0) for block0. Otherwise, on cannam@167: P processes, FFTW will return local_n0 equal to cannam@167: block0 on the first P / block0 processes (rounded down), cannam@167: return local_n0 equal to n0 - block0 * (P / block0) on cannam@167: the next process, and local_n0 equal to zero on any remaining cannam@167: processes. In general, we recommend using the default block size cannam@167: (which corresponds to n0 / P, rounded up). cannam@167: cannam@167: cannam@167:

For example, suppose you have P = 4 processes and

n0 =
cannam@167: 21

. The default will be a block size of 6, which will give cannam@167: local_n0 = 6 on the first three processes and

local_n0 =
cannam@167: 3

on the last process. Instead, however, you could specify cannam@167: block0 = 5 if you wanted, which would give local_n0 = 5 cannam@167: on processes 0 to 2, local_n0 = 6 on process 3. (This choice, cannam@167: while it may look superficially more “balanced,” has the same cannam@167: critical path as FFTW’s default but requires more communications.) cannam@167:

6.4.1 Basic and advanced distribution interfaces