
220 Energy-Aware Memory Management for EMSs
which yields the minimum index vector
x
y
min
= H
⎡
⎢
⎣
¯
i
¯
j
¯
k
⎤
⎥
⎦
min
+ u =
3
0
;
the distance between the A-elements A[3][0] and A[9][3] is 57.
In the linearization by column concatenation, the array indices are reversed.
Matrix T is thus
012
120
and u =
0
3
. The unimodular matrix S =
⎡
⎢
⎣
−21 4
10−2
00 1
⎤
⎥
⎦
and the Hermite Normal Form is:
H = T · S =
100
010
.
The new iterator polytope is:
¯
P =
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
⎡
⎢
⎣
¯
i
¯
j
¯
k
⎤
⎥
⎦
∈ Z
3
⎡
⎢
⎢
⎢
⎣
−21 4
10−2
00 1
8 −6 −19
⎤
⎥
⎥
⎥
⎦
⎡
⎢
⎣
¯
i
¯
j
¯
k
⎤
⎥
⎦
≥
⎡
⎢
⎢
⎢
⎣
0
0
0
−12
⎤
⎥
⎥
⎥
⎦
⎫
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎭
.
The (lexicographically) maximum iterator vector in
¯
P is
⎡
⎢
⎣
¯
i
¯
j
¯
k
⎤
⎥
⎦
max
=
⎡
⎢
⎣
8
0
4
⎤
⎥
⎦
,
which yields the maximum index vector
x
y
max
= H
⎡
⎢
⎣
¯
i