Optimization $(20$ points$)$

Consider the following code for calculating the dot product of two vectors of double

precision floating point numbers.

double dot$\_$prod$($double A$[],$ double B$[],$ int n$)\{$

int i;

double $r=0$;

for $r=r+A[i]***B[i]$;$r7$CPEr$=0r=r+(A[i]**B[i]+A[i+1]**B[i+1])$;$i++r=r+A[i]**B[i]$;$r\frac{7}{2}=3\mathrm{.}5$CPE;$i$; $i++(i=0$;$i$

$r=r+(A[i]**B[i]+A[i+1]**B[i+1])$;

for $($ ;$i$; $i++)$

$r=r+A[i]**B[i]$;

return $r$;

$\}$

$(5$ points$)$ What $is$ the theoretically optimal CPE for this loop?

$\frac{7}{2}=3\mathrm{.}5$CPE, since the critical path $is$ still addition, but now two elements will

$be$ added $in$ each iteration.