A processor with a two$-$level cache hierarchy employs hardware prefetching to

enhance performance. The L$1$ and L$2$ caches are $32$ KB and $64$ KB $,$ respectively, both

$8-$way set associative and $64$ B block size.

The hardware prefetcher observes memory access patterns and prefetches cache

lines into the L$2$ cache based on detected stride patterns. It can prefetch up to $4$

cache lines ahead of the current access. When a constant positive stride is detected,

it prefetches cache lines at addresses current$\_$address $+n*$ stride, where $n$

ranges from $1$ to $4.$

Consider a program that performs the following two operations:

Forward array access: accesses an array size of $1$ MB sequentially, reading one

$64-$byte element at a time in increasing address order.

Reverse array access: accesses another array of size $1$ MB in reverse order,

reading one $64-$byte element at a time in decreasing address order.