FFTW 3.3.5: Basic and advanced distribution interfaces

As with the planner interface, the ‘fftw_mpi_local_size’ cannam@127: distribution interface is broken into basic and advanced cannam@127: (‘_many’) interfaces, where the latter allows you to specify the cannam@127: block size manually and also to request block sizes when computing cannam@127: multiple transforms simultaneously. These functions are documented cannam@127: more exhaustively by the FFTW MPI Reference, but we summarize the cannam@127: basic ideas here using a couple of two-dimensional examples. cannam@127:

For the 100 × 200 complex-DFT example, above, we would find cannam@127: the distribution by calling the following function in the basic cannam@127: interface: cannam@127:

cannam@127:

ptrdiff_t fftw_mpi_local_size_2d(ptrdiff_t n0, ptrdiff_t n1, MPI_Comm comm,
cannam@127:                                  ptrdiff_t *local_n0, ptrdiff_t *local_0_start);
cannam@127:

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

n0 =
cannam@127: 100

and n1 = 200) and an MPI communicator (comm), this cannam@127: function provides three numbers. cannam@127:

First, it describes the shape of the local data: the current process cannam@127: should store a local_n0 by n1 slice of the overall cannam@127: dataset, in row-major order (n1 dimension contiguous), starting cannam@127: at index local_0_start. That is, if the total dataset is cannam@127: viewed as a n0 by n1 matrix, the current process should cannam@127: store the rows local_0_start to cannam@127: local_0_start+local_n0-1. Obviously, if you are running with cannam@127: only a single MPI process, that process will store the entire array: cannam@127: local_0_start will be zero and local_n0 will be cannam@127: n0. See Row-major Format. cannam@127: cannam@127:

Second, the return value is the total number of data elements (e.g., cannam@127: complex numbers for a complex DFT) that should be allocated for the cannam@127: input and output arrays on the current process (ideally with cannam@127: fftw_malloc or an ‘fftw_alloc’ function, to ensure optimal cannam@127: alignment). It might seem that this should always be equal to cannam@127: local_n0 * n1, but this is not the case. FFTW’s cannam@127: distributed FFT algorithms require data redistributions at cannam@127: intermediate stages of the transform, and in some circumstances this cannam@127: may require slightly larger local storage. This is discussed in more cannam@127: detail below, under Load balancing. cannam@127: cannam@127: cannam@127:

The advanced-interface ‘local_size’ function for multidimensional cannam@127: transforms returns the same three things (local_n0, cannam@127: local_0_start, and the total number of elements to allocate), cannam@127: but takes more inputs: cannam@127:

cannam@127:

ptrdiff_t fftw_mpi_local_size_many(int rnk, const ptrdiff_t *n,
cannam@127:                                    ptrdiff_t howmany,
cannam@127:                                    ptrdiff_t block0,
cannam@127:                                    MPI_Comm comm,
cannam@127:                                    ptrdiff_t *local_n0,
cannam@127:                                    ptrdiff_t *local_0_start);
cannam@127:

The two-dimensional case above corresponds to rnk = 2 and an cannam@127: array n of length 2 with n[0] = n0 and n[1] = n1. cannam@127: This routine is for any rnk > 1; one-dimensional transforms cannam@127: have their own interface because they work slightly differently, as cannam@127: discussed below. cannam@127:

First, the advanced interface allows you to perform multiple cannam@127: transforms at once, of interleaved data, as specified by the cannam@127: howmany parameter. (hoamany is 1 for a single cannam@127: transform.) cannam@127:

Second, here you can specify your desired block size in the n0 cannam@127: dimension, block0. To use FFTW’s default block size, pass cannam@127: FFTW_MPI_DEFAULT_BLOCK (0) for block0. Otherwise, on cannam@127: P processes, FFTW will return local_n0 equal to cannam@127: block0 on the first P / block0 processes (rounded down), cannam@127: return local_n0 equal to n0 - block0 * (P / block0) on cannam@127: the next process, and local_n0 equal to zero on any remaining cannam@127: processes. In general, we recommend using the default block size cannam@127: (which corresponds to n0 / P, rounded up). cannam@127: cannam@127: cannam@127:

For example, suppose you have P = 4 processes and

n0 =
cannam@127: 21

. The default will be a block size of 6, which will give cannam@127: local_n0 = 6 on the first three processes and

local_n0 =
cannam@127: 3

on the last process. Instead, however, you could specify cannam@127: block0 = 5 if you wanted, which would give local_n0 = 5 cannam@127: on processes 0 to 2, local_n0 = 6 on process 3. (This choice, cannam@127: while it may look superficially more “balanced,” has the same cannam@127: critical path as FFTW’s default but requires more communications.) cannam@127:

6.4.1 Basic and advanced distribution interfaces