$5\mathrm{.}1$ In this exercise we look at memory locality properties of matrix computation.

The following code is written in C$,$ where elements within the same row are stored

contiguously. Assume each word is a $64-$bit integer.

for $($I$=0$; I$<8$; I$++)$

for $($J$=0$; J$<8000$; J$++)$

A$[$I$][$J$]=$B$[$I$][0]+$A$[$J$][$I$]$;

A$)[5]<5\mathrm{.}1>$ How many $64-$bit integers can be stored in a $16-$byte cache

block?

B$)[5]<5\mathrm{.}1>$ Which variable references exhibit temporal locality?

C$)[5]<5\mathrm{.}1>$ Which variable references exhibit spatial locality?

Locality is affected by both the reference order and data layout. The same

computation can also be written below in Matlab, which differs from C in that it

stores matrix elements within the same column contiguously in memory.

for I$=1$:$8$

for J$=1$:$8000$

A$($I$,$J$)=$B$($I$,0)+$A$($J$,$I$)$;

end

end

D$)[5]<5\mathrm{.}1>$ Which variable references exhibit temporal locality?

E$)[5]<5\mathrm{.}1>$ Which variable references exhibit spatial locality?