Consider the function compute variance listed below, which computes the variance of

integer numbers stored in the array data.

$1$ int data$[$N$]$;

$2$

$3$ int compute$\_$variance$()\{$

$4$ int sum$1=0,$ sum$2=0,$ result;

$5$ int i;

$6$

$7$ for$($i$=0$; i $<$ N; i$++)\{$

$8$ sum$1+=$ data$[$i$]$;

$9\}$

$10$ sum$1/=$ N;

$11$

$12$ for$($i$=0$; i $<$ N; i$++)\{$

$13$ sum$2+=$ data$[$i$]*$ data$[$i$]$;

$14\}$

$15$ sum$2/=$ N;

$16$

$17$ result $=($sum$2-$ sum$1*$sum$1)$;

$18$

$19$ return result;

$20\}$

Suppose this program is executing on a $32-$bit processor with a direct$-$mapped cache

with parameters $($m$,$ k$,$ n$)=(32,3,3).$ S e e t h e F i g u r e $1$ f o r t h e

e x p l a n a t i o n o f m $,$ k $,$ a n d n $.$

F i g u r e $1$

We make the following additional assumptions:

$$ An int is $4$ bytes wide.

$$ sum$1,$ sum$2,$ result, and i are all stored in registers.

$$ data is stored in memory starting at address $0$x$0.$

Answer the following questions:

$($a$)$ How many blocks will be in the cache? $[10$ points$]$

$($b$)$ How many bytes$-$per$-$block will be in the cache? $[10$ points$]$

$($c$)$ Consider the case where N is $16.$ How many cache misses will there be$?$

This question is solved for you.

$($d$)$ Now suppose that N is $32.$ Based upon the above solution, recompute the number

of cache misses. $[30$ points$]$