... SPMD¹

Single Program, Multiple Data

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

... separate²

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

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

... though³

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

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

... entities⁴

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.

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

... group⁵

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.

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

... group⁶

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

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

... operation⁷

In fact it is neccessary to use a shift and copy operation because the source and destination arguments of shift must be distinct arrays. In the comment explaining the inner block matrix multiplication, by the way, the symbol b' means the original unshifted value of the array b.

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

... dimension⁸

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

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

... subscript⁹

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

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

... communications¹⁰

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.

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

... arrays¹¹

Incidentally, subranges, and particularly strided subranges, introduce an ambiguity in the definition of the shift operators + and - on locations. Is the numeric shift measured terms of subscript relative to the subrange or of the parent range? As a matter of definition, the shift is always in terms of subscript in the template range--the ultimate parent from which a subrange is derived (by zero or more stages of triplet subscripting).

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