Consider the following instruction execution sequence $($with instructions numbered for

convenience$).$ The table below shows the order in which two key pipeline stages $$ Rename and

Commit $$ occur for each instruction in the code segment. The processor is an R$10$K style design.

In the $$Rename Activity$$ column, please list the register rename actions taken in each row.

When allocating physical registers for renaming, please assume that the lowest numbered

physical register in the freelist is allocated. Further assume that initially, the registers r$1,$ r$2,$

and r$3$ are renamed to physical registers p$1,$ p$2,$ and p$3.$ Please remember that deallocated

physical registers must be put back in the freelist. Assume as many physical registers as you

need from p$4$ onwards.

$1$: Add r$3,$ r$1,$ r$2$

$2$: Add r$2,$ r$3,$ r$1$

$3$: Add r$1,$ r$3,$ r$2$

$4$: Add r$3,$ r$3,$ r$2$

$5$: Add r$2,$ r$2,$ r$2$

$6$: Add r$1,$ r$2,$ r$3$ IV$.$ Out$-$of$-$order Execution $(25$ points$)$

$($a$)$ Consider the following instruction execution sequence $($with instructions numbered for

convenience$).$ The table below shows the order in which two key pipeline stages $-$ Rename and

Commit $-$ occur for each instruction in the code segment. The processor is an R$10$K style design.

In the "Rename Activity" column, please list the register rename actions taken in each row.

When allocating physical registers for renaming, please assume that the lowest numbered

physical register in the freelist is allocated. Further assume that initially, the registers r$1,$ r$2,$

and r$3$ are renamed to physical registers p$1,$ p$2,$ and p$3.$ Please remember that deallocated

physical registers must be put back in the freelist. Assume as many physical registers as you

need from p$4$ onwards.

Add r$3,$ r$1,$ r$2$

Add r$2,$ r$3,$ r$1$

Add r$1,$ r$3,$ r$2$

Add r$3,$ r$3,$ r$2$

Add r$2,$ r$2,$ r$2$

Add r$1,$ r$2,$ r$3$

Add r$1,$ r$1,$ r$2$

Add r$1,$ r$1,$ r$3$

$($b$)(3$ points$)$ Can we infer that the processor is an in$-$order processor if all renames and commits

happen in program order $($as in the example above$)?$ Justify your answer $(1-2$ sentences at most$).$

$7$: Add r$1,$ r$1,$ r$2$

$8$: Add r$1,$ r$1,$ r$3$