$2.[20$ marks$]$ Power and Performance

Imagine a homogeneous multicore processor where each core has a performance

of $9$ TFs$/$s and a power dissipation of $4$ W$.$ There are two options to scale

this processor's performance by a $\_$multiplicative$\_$ factor of sigma: either

i$)$ scale the number of cores that are running. i$.$e$.,$ powered on$,$ by the

factor sigma, or ii$)$ scale the clock frequency by the factor sigma $($the

voltage will scale by roughly the same amount$).$

In option i$),$ the power of the chip will scale by the factor sigma. In

option ii$),$ the power of the chip will scale, say, by the factor sigma$^2\mathrm{.}712.$

We can increase or decrease the number of running cores, or we can increase

or decrease the clock frequency.

a$)$ Let sigma $=4($want more performance$).$ State the new performance, power,

and power efficiency, for each option. Which option is better? Why?

b$)$ Let sigma $=1/4($want less performance$).$ State the new performance, power,

and power efficiency, for each option. Which option is better? Why?

Note: The units of power efficiency are GFs$/$s$/$W$.$