Consider a $64-$bit computer featuring a simplified memory hierarchy. This

hierarchy comprises a solitary cache and an unbounded backing memory. The cache is defined by

the following attributes:

$$ Direct$-$Mapped, Write$-$through, Write allocate.

$$ Cache blocks are $8$ words each.

$$ The cache has $128$ sets.

$($a$)$ Consider the provided code snippet in the C programming language intended for execution

on the previously described computer. Assume the following conditions: program instructions are

not stored in the cache, arrays are aligned with the cache $($starting at the beginning of a cache

line$),$ integers are $32$ bits, and all other variables are exclusively stored in registers.

int N $=32859$; int

A$[$N$]$;

for $($int i $=0$; i $<$ N; i $+=2)\{$

A$[$i$]=$ A$[$i$+1]$; $\}$

Determine the following:

$($i$)$ The number of cache misses.

$($ii$)$ The cache miss rate.

$($iii$)$ The type of cache misses that occur.

$($b$)$ Consider the following code fragment in the C programming language to be run on the

described computer. Assume that: program instructions are not stored in cache, arrays are cachealigned $($the beginning of the array aligns with the beginning of a cache line$),$ ints are $32$ bits, and

all other variables are stored only in registers.

int N $=32859$; int

A$[$N$]$; int B$[$N$]$;

for $($int i $=0$; i $<$ N; $++$i$)\{$ B$[$i$]=$ A$[$i$]$;

$\}$

Determine the following:

$($i$)$ The number of cache misses.

$($ii$)$ The cache miss rate.

$($iii$)$ The type of cache misses that occur.