$(4)3$M decides to make Post$-$its by printing yellow squares on white pieces of

paper. As part of the printing process, they need to set the CMYK $($cyan$,$

magenta, yellow, black$)$ value for every point in the square. $3$M hires you

to determine the efficiency of the following algorithms on a machine with a

$2,048-$byte direct$-$mapped data cache with $32-$byte blocks. You are given the

following definitions:

$1$ struct point color $\{$

$2$ int c;

$3$ int m;

$4$ int y;

$5$ int k;

$\}$;

$6$ struct point color square$[16][16]$;

$7$ int i$,$ j;

Assume the two functions are executed under the following conditions:

$$ sizeof$($int$)=4$

$$ square begins at memory address $0.$

$$ The cache is initially empty.

$$ The only memory accesses are to the entries of the array square. Vari$-$

ables i and j are stored in registers.

A$.[1+4+1]$

$1$ for $($i $=0$; i $<16$; i$++)\{$

$2$ for $($j $=0$; j $<16$; j$++)\{$

$3$ square$[$i$][$j$].$c $=0$;

$4$ square$[$i$][$j$].$m $=0$;

$5$ square$[$i$][$j$].$y $=1$;

$6$ square$[$i$][$j$].$k $=0$;

$7\}$

$8\}$

$($a$)$ What is the total number of writes? Explain.

$($b$)$ What is the total number of writes that miss in the cache? Explain.

$($c$)$ What is the miss rate? Explain.

$4$

B$.[1+4+1]$

$1$ for $($i $=0$; i $<16$; i$++)\{$

$2$ for $($j $=0$; j $<16$; j$++)\{$

$3$ square$[$i$][$j$].$y $=1$;

$4\}$

$5\}$

$6$ for $($i $=0$; i $<16$; i$++)\{$

$7$ for $($j $=0$; j $<16$; j$++)\{$

$8$ square$[$i$][$j$].$c $=0$;

$9$ square$[$i$][$j$].$m $=0$;

$10$ square$[$i$][$j$].$k $=0$;

$11\}$

$12\}$

$($a$)$ What is the total number of writes? Explain.

$($b$)$ What is the total number of writes that miss in the cache? Explain.

$($c$)$ What is the miss rate? Explain