
Computation of Data Storage Requirements 77
i
1
,... ,i
n
, is characterized by an iterator space and an index (or array) space.
The iterator space signifies the set of all iterator vectors i =(i
1
,... ,i
n
) ∈ Z
n
in the scope of the array reference. The index space is the set of all index
vectors x =(x
1
,... ,x
m
) ∈ Z
m
of the array reference. When the indices of
an array reference are linear mappings with integer coefficients of the loop
iterators, the index space consists of one or several linearly bounded lattices
(LBLs) [10]—the image of an affine vector function over the iterator polytope
A · i ≥ b:
{x = T · i + u ∈ Z
m
|A · i ≥ b, i ∈ Z
n
} (3.1)
where x ∈ Z
m
is