Information Technology Reference
In-Depth Information
TABLE 4.10:
The Interval-based Core-switching Approach Selects P1 in the First Interval
and P2 in the Second with Oracle Knowledge. The Resulting EDP (18) is Worse Than Either
P1 or P2 Running Both Intervals (EDP of 16.2 and 16.4, Respectively). Adapted from [
198
].
P1
P2
Best
EDP Core
Interval
Energy
Time
EDP
Energy
Time
EDP
1
1
4
4
2
2.1
4.2
P1
2
1
4.1
4.1
2
2
4
P2
Overall
2
8.1
16.2
4
4.1
16.4
(1
+
2)
×
(4
+
2)
=
18
oracle knowledge, the overall EDP for the whole application may turn out to be far from
optimal. Sazeides, Kumar, Tullsen, and Constantinou investigated the matter further and
realized that
it is not possible to guarantee EDP—or for that matter ED
2
P—optimization with
any interval-based approach where local, per-interval, decisions are taken
[
198
]. The root of
the problem is that choosing the smallest energy-delay
product
(or energy-delay
2
product)
regardless of the magnitude of its factors may result in globally sub-optimal decisions. To
illustrate the problem the core switching example in Table 4.10 shows how the interval-
based approach, while choosing the best core (best EDP) per-phase, fails to optimize the
global EDP:
More
formally,
optimizing
EDP
for
an
application
is
equivalent
to
solving:
MIN (
E
t
), where
E
is the energy spent during the application execution time
t
.
Dividing application execution into
n
intervals, the problem becomes
×
MIN
E
i
t
i
n
n
×
,
i
=
1
i
=
1
where
E
i
and
t
i
are the energy and duration, respectively, of interval
i
.
If there are
several
choices in interval
i
for the pair
E
i
and
t
i
(for example,
several
core
switching choices), then choosing option
j
in interval
i
is denoted by
E
j
i
and
t
j
i
.
In this case, optimizing EDP
individually per interval
is equivalent to finding the
j
for each
i
such as each
product term of the sum
is minimal:
n
MIN
E
ji
t
j
i
.
×
i
i
=
1
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