$1(20$ points$)$

Consider three different processors P$1,$ P$2,$ and P$3$ executing the same instruction set. P$1$ has a $3\mathrm{.}2$ GHz clock

rate and a CPI of $1\mathrm{.}5.$ P$2$ has a $2\mathrm{.}0$ GHz clock rate and a CPI of $1\mathrm{.}0.$ P$3$ has a $4\mathrm{.}0$ GHz clock rate and has a CPI

of $2\mathrm{.}3.$

$1\mathrm{.}1(7$ points$)$

Calculate the performance of each processor expressed in instructions per second.

$1\mathrm{.}2(7$ points$)$

If each of these processors executes a program in $10$ seconds, calculate the number of cycles and the number of

instructions.

$1\mathrm{.}3(6$ points$)$

We are trying to reduce the execution time of P$2$ by $30\%,$ but this leads to an increase of $20\%$ in the CPI. What

should the clock rate be to obtain this reduction in execution time?

$1$

$2(20$ points$)$

Consider two different implementations of the same instruction set architecture. The instructions can be divided

into four classes according to their CPI $($classes A$,$ B$,$ C$,$ and D$).$ P$1$ with a clock rate of $2\mathrm{.}5$ GHz and CPIs of $1,$

$2,3,$ and $3$ for the corresponding classes, and P$2$ with a clock rate of $3$ GHz and CPIs of $2,2,2,$ and $2.$ Given

a program with a dynamic instruction count of $1\mathrm{.}0$e$6$ instructions divided into classes as follows: $30\%$ class A$,$

$20\%$ class B$,30\%$ class C$,$ and $20\%$ class D:

$2\mathrm{.}1(7$ points$)$

What is the total CPI for each implementation?

$2\mathrm{.}2(7$ points$)$

Calculate the clock cycles required in both cases.

$2\mathrm{.}3(6$ points$)$

Which is faster: P$1$ or P$2?$

$2$

$3(20$ points$)$

In this exercise we look at memory locality properties of matrix computation. The following code is written in

C$,$ where elements within the same row of a matrix are stored contiguously. You can assume that undefined

symbols are primitive types, i$.$e$.,$ int, double etc.

$1$ for$($ int j $=1$; j $<$ n$-1$; j$++)\{$

$2$ for$($int i $=1$; i $<$ m$-1$; i$++)\{$

$3$ Anew$[$j$][$i$]=0\mathrm{.}25*($A$[$j$][$i$+1]+$ A$[$j$][$i$-1]+$ A$[$j$-1][$i$]+$ A$[$j$+1][$i$])$;

$4$ err $=$ max$($err$,$ fabs$($Anew$[$j$][$i$]-$ A$[$j$][$i$])$;

$5\}$

$6\}$

$3\mathrm{.}1(7$ points$)$

Which variables exhibit temporal locality?

$3\mathrm{.}2(7$ points$)$

Which variables exhibit spatial locality? Locality is affected by both the reference order and data layout.

$3\mathrm{.}3(6$ points$)$

Would the program be slower or faster if the outer loop iterated over i and the inner loop iterated over j$?$ Why?

$3$

$4(20$ points$)$

Consider a byte addressing architecture with $64-$bit memory addresses.

$4\mathrm{.}1(5$ points$)$

Which bits of the address would be used in the tag, index and offset in a direct$-$mapped cache with $5121-$word

blocks?

$4\mathrm{.}2(5$ points$)$

Which bits of the address would be used in the tag, index and offset in a direct$-$mapped cache with $648-$word

blocks?

$4\mathrm{.}3(5$ points$)$

What is the ratio of bits used for storing data to total bits stored in the cache in each of the above cases?

$4\mathrm{.}4(5$ points$)$

Which bits of the address would be used in the tag, index and offset in a two$-$way set associative cache with

$1-$word blocks and a total capacity of $512$ words.

$4$