Problem $2(2$ pts$)$

for $($r $=0$; r $$ R; r$++)$

for $($q $=0$; q $$ Q; q$++)$

for $($p $=0$; p $$ P; p$++)$

for $($s $=$O; s $$ S; st$+)$

sum$[$r$][$p$][$g$]+=$ A$[$r$][$s$][2$g$]*$ C$4[$s$][$r$]$;

For the same code above, calculate the spatial reuse direction vector for array reference A$.$ Consider

then two cases, when a cache line fits $4$ elements of A$\text{'}$s datatype and when the cache line fits $2$

elements of A$\text{'}$s type. In which scenario will spatial reuse be possible?

Show the steps taken, include the matrix access representation of reference $A,$ the solution to the linear

system to determine the reuse$-$direction vector, and explain the meaning of the direction vector found.