Problem $1$:

Consider the following computation: $,F=(Axy+Byz-Czx)(A+B-C)$

Suppose we wish to implement this computation using a multifunction pipeline consisting of two MUL$-$

TIPLY stages, one ADD stage and one SUBTRACT. The scheduling diagram for one iteration of this

computation is shown next.

Figure $1$: Pipeline $1$ Scheduling Diagram

a$)$ Construct a reservation table for this pipeline $($pipeline$1)$ assuming availability of $2$ MULTIPLYers,

one ADDer and one SUBTRACTor. Find an optimal latency cycle for iterating $200$ computations on

pipeline$1.$

b$)$ To improve performance, we are going to use a $2-$stage MULTIPLYer unit. We still assume $2$ MUL$-$

TIPLYers, one ADDer and one SUBTRACTor. Under the new arrangements, construct a new scheduling

diagram and a new reservation table for this pipeline $($pipeline$2).$ Find an optimal latency cycle for $400$

iterations on pipeline$2.$ How do the speedups of pipeline$1$ and pipeline $2$ compare?

c$)$ Let's assume each ADDer and SUBTRACTor has about $200$ns delay and the original single$-$stage

MULTIPLYer has $500$ns delay. After partitioning, each MULTIPLY stage has about $250$ns delay. Under

these assumptions, which pipeline is potentially faster, after all?