Modeling, Simulation, and Measurement - Computer Architecture Techniques for Power-Efficiency - page 10

example, energy-per-instruction (EPI) is sometimes used as a method of comparing energy
optimizations, particularly those that focus on general microarchitectural traits, rather than on
the runtime of a particular application.
Energy-delay product : While low power often used to be viewed as synonymous with lower
performance, that is no longer the case. In many cases, application runtime is of significant
relevance even in energy- or power-constrained environments. With the dual goals of low
energy and fast runtimes in mind, energy-delay product (EDP) was proposed as a useful metric
[ 85 ]. EDP offers equal “weight” to either energy or performance degradation. If either energy or
delay increase, the EDP will increase. Thus, lower EDP values are desirable. When comparing
scenarios that do not alter the instruction count or mix, EDP is roughly equivalent to the
reciprocal of MIPS 2 /Watt. Note the derivation below:

Delay = runtime

Energy = Watts ∗ runtime

EDP = Watts ∗ runtime ∗ runtime.

runtime = Instruction Count / MIPS

(ICount / MIPS) 2 EDP = Watts ∗

ICount 2 1/(MIPS 2 EDP = ∗ / Watt).

Unlike EPI, EDP's inclusion of runtime means that this is a metric that improves for
approaches that either hold energy constant but execute the same instruction mix faster , or hold
performance constant but execute at a lower energy, or some combination of the two.
Energy-delay-squared and beyond : Following on the original EDP proposal, other work
has suggested alternative metrics, such as energy-delay-squared product (ED 2 P) or energy-
delay-cubed product (ED 3 P) [ 211 , 251 ]. These alternatives correspond to MIPS 3 per Watt or
MIPS 4 per Watt. At a qualitative level, one can view these metrics as applying to the high-
performance arena where performance improvements may matter more than energy savings.
Delving deeper into these metrics, one can argue that ED 2 P makes the most sense
when considering fixed microarchitectures, but accounting for voltage scaling as a possible
energy management technique. In particular, consider the following rough trends: power is
proportional to CV 2 f , which for a fixed microarchitecture and design is proportional to V 3 .
Performance, on the other hand, is roughly proportional to frequency. Since frequency varies
roughly linearly with voltage in the 1-3 V range, this means that performance is also roughly
proportional to voltage. As a result, when processors use voltage scaling as a primary power-
performance trade-off, metrics considering (perf ) 3 / power are the fair way to compare energy
efficiencies. This, in fact, is ED 2 PorMIPS 3 /Watt.
The broader question of how to weigh energy and performance is often answered specif-
ically in regards to particular designs, or even to particular modules and decisions within a