For a $64-$Kbyte, $2-$way set associative cache, calculate the cache miss rate for the following loop. Make the following assumptions:

$1.$ There is no entry in the cache initially;

$2.$ Integers are $4$ bytes long and two$-$dimensional arrays are stored in row$-$major order.

int array$[32][1024]$; $//$ An integer array with $32$ rows and $1024$ columns

$```$

for $($int i $=0$; i $<mtext></mtext><mn>3</mn><mn>2</mn>$; i$++)\{$

for $($int j $=0$; j $<mtext></mtext><mn>1</mn><mn>0</mn><mn>2</mn><mn>4</mn>$; j$++)\{$

array$[$i$][$j$]=($array$[$i$][$j$]+$ array$[31-$ i$][1023-$j$])/2$;

$\}$

$\}$

$```$

a$.$ What is the cache miss$-$rate for $32-$byte cache blocks?

b$.$ What is the cache miss$-$rate for $16-$byte cache blocks?

c$.$ Can you re$-$write the program, so that the final program performs the same computations and memory accesses but with fewer cache misses.