Question $1$

The following code computes $Y[i]=a**x[i]+Y[i]$ for an array of length $100$ doubles. Initially, $R1=$ address of $x,R2=$ address of $Y,$ and $F0$ contains a$.$

ADDIU R$3,$ R$1,800$

; $R3=$ address of $x+100$ doubles

loop:

L$.$D F$2,0($R$1)$

MUL.D F$4,$ F$2,$ F$0$

L$.$D F$6,$ O$($R$2)$

ADD.D F$6,$ F$4,$ F$6$

S$.$D F$6,$ O$($R$2)$

ADDIU R$1,$ R$1,8$

ADDIU R$2,$ R$2,8$

BNE R$1,$ R$3,$ loop

; load F$2=$ X$[$i$]$

; $F4=a^{**}x[i]$

; load F$6=$ Y$[$i$]$

; F$6=a^{**}x[i]+Y[i]$

; store F$6$

; increment $x$ pointer

; increment $Y$ pointer

; loop if $($R$1!=$ R$3)$

Assume the following functional unit latencies $($given as stall cycles before use$).$ The loop branch is predicted to be always taken with zero delay.

$\backslash$table$[[$Instruction producing result,Instruction using result,Stall cycles before use$],[$FP operation,Another FP operation,$3$ stall cycles$],[$FP operation,FP store,$2$ stall cycles$],[$FP load,FP operation,$2$ stall cycles$],[$Integer ALU operation,Another ALU operation,$0$ stall cycles$]]$

a$)$ Assume a single$-$issue pipeline. Show the loop code including the stall cycles. What is the number of cycles per iteration to compute one element of the array Y$?$

b$)$ Unroll the loop Two times and schedule it to reduce stall cycles, collapsing the loop overhead instructions. Show the instruction schedule. What is the average number of cycles to compute one element of the array Y$?$