Ex$3$: Consider the following loop, where x$,$ y$,$ z$,$ w$,$ and output are vectors of equal length:

for $($i $=0$; i $<500$; $++$i$)$

$\{$

output$[$i$]=($x$[$i$]+3*$y$[$i$])*($z$[$i$]-2*$w$[$i$])$;

$\}$

a$)$ Convert the loop into Vector MIPS code with appropriate comments explaining each step.

b$)$ Estimate the number of scalar MIPS instructions needed to execute the loop without vectorization.

c$)$ Explain the advantages of vectorizing this code and how it improves performance over the scalar version

Ex$4$: Instruction Sequence:

$1.$ Addi $t$0,$ $t$0,10$ ; $t$0=$ $t$0+10$

$2.$ Lw $t$1,0($$t$0)$ ; $t$1=$ Mem$[$$t$0]$

$3.$ Sub $t$2,$ $t$0,$ $t$1$ ; $t$2=$ $t$0-$ $t$1$

$4.$ Mul $t$3,$ $t$1,$ $t$2$ ; $t$3=$ $t$1*$ $t$2$

$5.$ Add $t$4,$ $t$2,$ $t$3$ ; $t$4=$ $t$2+$ $t$3$

a$.$ List all the data dependencies and their types $($RAW$,$ WAR, WAW$).$

b$.$ Assuming the sequence is executed correctly and that the initial values of $t$0,$ $t$1,$ $t$2,$ $t$3,$ and $t$4$ are $100,200,50,30,$ and $0$ respectively, what will be the final values of $t$0,$ $t$1,$ $t$2,$ $t$3,$ and $t$4?$ Assume memory location $110$ contains the value $300.$

c$.$ Assuming there are neither forwarding nor hazard detection units, what will be the final values of $t$0,$ $t$1,$ $t$2,$ $t$3,$ and $t$4$ in this case?

d$.$ Explain how branch prediction works in MIPS architecture and what role it plays in pipelining.