struct algae

$\_$

position

$\{$

$$ float x;

$$ float y;

$\}$

;

$$ struct algae

$\_$

position grid

$[16][16]$

;

$$ float total

$\_$

x

$=$

$0$

$,$

$$total

$\_$

y

$=$

$0$

;

$$ int i

$,$

j;

You should also assume the following:

$$

$$sizeof

$($

float

$)$

$=$

$=$

$4$

$.$

$$

$$grid begins at memory address

$0$

$.$

$$

$$The cache is initially empty.

$$

$$The only memory accesses are to the entries of the grid array grid. the variables i

$,$

$$j

$,$

$$total x

$,$

$$total y are stored in registers.

We consider the following code:

$$ for

$($

i

$=$

$0$

; i

$<$

$16$

; i

$+$

$+$

$)\{$

$$ for

$($

j

$=$

$0$

; j

$<$

$16$

; j

$+$

$+$

$)\{$

$$ total

$\_$

x

$+$

$=$

$$grid

$[$

j

$][$

i

$]$

$.$

x;

$$ total

$\_$

y

$+$

$=$

$$grid

$[$

j

$][$

i

$]$

$.$

y;

$\}\}$Analyze the cache performance of this code $($provide some short explanations so we see how you got the result; it helps to draw the cache$)$:

$($a$)$ What is the total number of reads?

$($b$)$ What is the total number of reads that miss in the cache?

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

$($d$)$ What would the miss rate be if the cache were twice as big?