In this problem, we are going to study how adding an increasing number of cores in a practical system

modifies its speedup.

Assume a single core has the following CPIs for each class of instructions:

Arithmetic $=2$

Load$/$Store $(\frac{L}{S})=15$

Branch $=5$

Each core runs on a $2GHz$ clock frequency

Also assume that we are executing a program in our system comprising the following number of

instructions:

Arithmetic $=2\mathrm{.}56E9($this is the same as writing $2\mathrm{.}56**{10}^9)$

Load$/$Store $(\frac{L}{S})=1\mathrm{.}28E9$

Branch $=2\mathrm{.}56E8$

Now, assume that, as the program is parallelized to run over multiple cores, the number of arithmetic

and load$/$store instructions per core is divided by $(0\mathrm{.}9p),$ where $p$ is the number of cores, but the

number of branch instructions per processor remains the same. So$,$ for example, if $p=2,$ we divide the

arithmetic and $\frac{L}{S}$ instructions per core by $0\mathrm{.}9**2=1\mathrm{.}8$ each but keep branch instructions the same.

$($Ideally$,$ we would divide the above parallelable instructions just by p; but sometimes in real life, even

the same class of instructions cannot be fully parallelized, hence the divide by $0\mathrm{.}9**p$ instead in this

example$)$

A$)$ Find the total execution time for this program on $p=1,2$ and $4$ cores, and show the relative speedup

of the $2$ and $4$ cores result relative to the single core result. Accordingly, fill up the values in the table

provided below $(5$pts$)$

B$)$ If the CPI of ONLY the Load$/$Store instructions was doubled, what would the impact be on the

execution time of the program on $p=1,2,4$ processors? $(2$ pts$)$

C$)$ What should the CPI of load$/$store instructions be reduced to in order for a modified single$-$core processor

to match the performance of a four$-$core processor using the original CPI values? Hint: Equate the two

different execution times and solve for the load$/$store CPI $(3$ pts$)$