A subrange is a section of a range, parametrized by a subscript triplet. Logically a subrange can be viewed as a subset of the locations of the original range. Subranges are members of the class Range. Because locations in a subrange are locations of the parent range, subranges retain an alignment relation to their parent range. Note that the integer subscripts for a subrange are in the range where is the extent of the subrange. See figure 6.
A triplet-subscripting syntax is used for creation of subranges:
if x is a range, then
x [0 : 49] is a contiguous subrange
x [1 : 98 : 2] is a strided subrange.
As a first application of subranges, we can uses strided subranges to
transform the Jacobi update of the previous section to a more
efficient red-black form. The result is shown in figure 7.
The iteration is split into two phases, the first with parity
and the second with parity . The range of the
inner over construct is either
y [0 : : 2] or
y [1 : : 2],
according to whether the global x index of the outer loop
has the same or different parity (odd/even) as the current phase.
This version eliminates all temporary
As a second application involving subranges, figure 8
is a parallel version of Cholesky decomposition. In pseudocode the
Some final comments on subranges. Creating a triplet subscripted section of a distributed array implicitly creates subranges of the ranges in the parent array. Also, arrays can be created directly with subranges, as in
Range xs = x [0 : 50] ; Range ys = y [1 : 198 : 2] ; int [[#,#]] e = new int [[xs, ys]] ;In HPF terms, e has a non-trivial linear alignment to the template spanned by x and y. By allowing subranges (and subgroups, see section 9) to appear in array constructors we reproduce the two-level alignment model of HPF in full generality, at little cost in terms of syntax extensions.