
52 Energy-Aware Memory Management for EMSs
x
i
x
j
x
j
x
i
lb
ub
X + Line (0, 1) X
Figure 2.11 Adding a line to project out an index.
loops. This is illustrated in Figure 2.11 where x
i
is an outer loop variable
and x
j
is an inner loop variable. To compute the loop bounds for the x
i
–loop
as a function of parameters and outer loop variables, the inner loop vari-
ables x
j
,j >i must be removed from the domain. This is done by projecting
the domain in the direction of the inner loop variables onto the x
i
-axis, giv-
ing lb and ub as the lower and upper bounds of x
i
, respectively. This can
be accomplished using convex union by adding a polyhedron consisting of a
set of ...