[MPICH] MPI_Dimms_create() and square numbers

[Andrea Di Blas]

hello,


I am wondering about the strategy implemented by MPI_Dimms_create() to
best balance the grid size in all dimensions.


for instance, when sizing a bidimensional cartesian communicator with a
square number p of processes, without enforcing constraints, sometimes the
two sizes are the sqrt(p) as (I would have) expected (e.g. with p = 4 or p
= 16), while other times they are not (e.g. with p = 9 or p = 100).
the same behavior happenes with cubes.

I wonder if I am doing something wrong, or if it is intentional, and if it
is so, why.  thanks in advance.


regards,


	andrea


/*---------------------------------------------------------*/
CODE: (for the cube case)


for(i = 2; i < 12; ++i)
{	grid_size[0] = grid_size[1] = 0; grid_size[2] = 0;
	MPI_Dims_create(i*i*i, 3, grid_size);
	printf("\nMPI_Dims_create(%4d, 3, grid_size) = %3d, %3d, %3d", i*i*i,
			grid_size[0], grid_size[1], grid_size[2]);
}



OUTPUT: (for the square case)

MPI_Dims_create(  4, 2, grid_size) =  2, 2
MPI_Dims_create(  9, 2, grid_size) =  9, 1
MPI_Dims_create( 16, 2, grid_size) =  4, 4
MPI_Dims_create( 25, 2, grid_size) = 25, 1
MPI_Dims_create( 36, 2, grid_size) = 18, 2
MPI_Dims_create( 49, 2, grid_size) = 49, 1
MPI_Dims_create( 64, 2, grid_size) =  8, 8
MPI_Dims_create( 81, 2, grid_size) =  9, 9
MPI_Dims_create(100, 2, grid_size) = 50, 2
MPI_Dims_create(121, 2, grid_size) = 121, 1


OUTPUT: (for the cube case)

MPI_Dims_create(   8, 3, grid_size) =   4,   2,   1
MPI_Dims_create(  27, 3, grid_size) =   9,   3,   1
MPI_Dims_create(  64, 3, grid_size) =   4,   4,   4
MPI_Dims_create( 125, 3, grid_size) = 125,   1,   1
MPI_Dims_create( 216, 3, grid_size) = 108,   2,   1
MPI_Dims_create( 343, 3, grid_size) = 343,   1,   1
MPI_Dims_create( 512, 3, grid_size) =   8,   8,   8
MPI_Dims_create( 729, 3, grid_size) =   9,   9,   9
MPI_Dims_create(1000, 3, grid_size) = 500,   2,   1
MPI_Dims_create(1331, 3, grid_size) = 1331,   1,   1



-- 
Andrea  Di Blas                     UCSC
                   School of Engineering
Tel: (831) 459 4193  Fax: (831) 459 4829