Now, you are given $3$ processors $A,B,C,$ and $5$ benchmark programs $P1$ to $P5.$ The following summarizes

the run time of these programs in the $3$ processors. In all cases, both the raw CPU times $($in seconds$)$

and the normalized time relative to processor A are shown. HINT: use a spreadsheet program to help

with answering this question.

A$\mathrm{.}2\mathrm{.}1$ Consider the first $3$ benchmark programs $(P1$ to $P3)$ only in this part. For each processor,

compute the following:

$($i$)$ Arithmetic mean of raw CPU time of the benchmark programs;

$($ii$)$ Geometric mean of raw CPU time of the benchmark programs;

$($iii$)$ Arithmetic mean of normalized CPU time of the benchmark programs;

$($iv$)$ Geometric mean of normalized CPU time of the benchmark programs;

$($v$)$ Total raw CPU time;

$($vi$)$ Total normalized CPU time;

A$\mathrm{.}2\mathrm{.}2$ Follow up from previous part. Examine the benchmark results closely, and you will notice that

processor $A,B,$ and $C,$ is fastest in exactly $1$ of the $3$ benchmark. As a result, a reasonable conclusion

is that all three processors are equally good.

Now, consider each of $6$ results you obtained in A$\mathrm{.}2\mathrm{.}1$ and answer the following:

What is the conclusion that each metric is suggesting? For example, consider the total run time of

the $3$ programs, which processor is fastest?

Which metric gives you the answer that the $3$ processors perform equally well?

Which metric would you choose to use for a fair comparison of the performance of the processors?

A$\mathrm{.}2\mathrm{.}3$ Now, repeat the previous $2$ questions but with benchmark programs $P1$ to $P4.$ That is$,$ you add

benchmark program $P4$ into the mix and recompute the results in various metrics.

You would notice that Processor $C$ is fastest in program $P4.$ As a result, considering all $4$ programs, a

reasonable conclusion is that since $C$ is fastest in $2$ programs, while A and $B$ are fastest in only $1,$ then

$C$ should be the fastest processor. Which of the metrics gives you this conclusion?

However, if you consider all $6$ different ways of comparison, some of them may lead to a different conclu$-$

sion that may also be reasonable. What other processor can you argue is having the best performance

when considering $P1$ to $P4?$

A$\mathrm{.}2\mathrm{.}4$ Now, if you consider only $P1$ to $P3$ and $P5($i$.$e$.,$ skipping $P4),$ how would that affects your above

conclusions? Note the runtime values of $P5$ are exactly $10000$ times of $P4.$

A$\mathrm{.}2\mathrm{.}5$ Considering using benchmark $P1$ to $P5,$ plus ONE ADDITIONAL benchmark of your choice

$(P6),$ is there a way to make Processor B stands out as being the fastest? If yes, let the run time of $P6$

in processor $A,B,C,$ be $t_A,t_B,t_C$ respectively, suggest values of $t_A,t_B,t_C$ and the performance metric

to use that will make Processor $B$ become fastest. If it is impossible, explain why is it the case.