h$-$is$-$problem tests

given the f

$11$

$.$ your ability to pr d$.$o owmg code to analyze: e ict the cache behavior of C

co

d

e$.$

Youti

$1.$

$2$

mt

X $[2][128].$

int

i $\text{'}$

$\text{'}$

Homework Problems

$3$

int

sum$=$

O;

$4$

$5$

for

$($i

$=$

O;

i $<$

$128$;

i$++)$

$\{$

$6$ sum $+=$ x $[$O$]$

$[$i$]$

$*$

X$[1]$

$[$i$]$;

$7\}$

Assume we execute this under the follow$$

ct

$$mg con $1$ttons:

$.\backslash$

$$

sizeof$($int$)$

$=4.$

$$ Array x begins at memory address

OxO

and is stored in row$-$major order.

$$ In each case below, the cache

is

initially empty.

$$ The only

~emory

accesses are to the entries of thy array x$.$ All other variables

are stored m registers. $1,-,$

$\_$;

i

Given these assumptions, estimate the miss rates for the following cases:

A$.$ Case

$1$:

Assu$1?$e the cache is $512$ bytes, direct$-$mapped, with $16-$byte cache

blocks.

What

$1$s

the miss rate?B$.$

Case

$2$:

What

is the miss rate if we double the cache size to $1,024$ bytes?

C$.$

Case $3$: Now assume the cache is $512$ bytes, two$-$way set associative using

an

LRU

replacement policy, with $16-$byte cache blocks. What

is

the cache

miss rate? $$

D$.$ For case $3,$ will a larger cache size help to reduce the miss rate? Why

or

why not?

E$.$ For case $3,$ will a larger block size help to reduce the miss rate? Why

or

why

not?