... separate¹

The run-time representation of our multi-dimensional arrays includes extra descriptor information that would simply encumber the large class ``non-scientific'' Java applications.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... though²

For example, c allows section subscripting, whereas d does not.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... entities³

Unless a section appears as an actual argument to a procedure, in which case the dummy argument names that section, or it is the target of a pointer assignment.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... group⁴

There is no cooperation between the two constructor calls for p and q, so an individual physical process might occur in both groups or in neither. As an option not illustrated here, vectors of ids can be passed to the Procs constructors to specify exactly which processes are included in a particular group.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... group⁵

The on clause can be omitted in some circumstances--see section 5.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... dimension⁶

Other higher-level ranges include CyclicRange, which produces the equivalent of CYCLIC distribution format in HPF.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... subscript⁷

But the effect of such subscripting is only well-defined inside an over construct parametrised by the index in question.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... specified)⁸

Formally | is being used here as an operator that combines a range and a triplet to return an object of the iterator class Index.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... communications⁹

Laplace's equation with cyclic boundary conditions is not particularly useful, but it illustrates the language features. More interesting boundary conditions can easily be incorporated later. Incidentally, this is a suitable place to mention that the array arguments of shift must be aligned arrays--they must have identical distributed ranges.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.