Two computers have 12-stage fetch-execute cycles where branches are determined i

Question

Two computers have 12-stage fetch-execute cycles where branches are determined in stage 5. One computer is pipelined with a pipeline latency of t_ p = 1 and the other is not pipelined. We are running a program of 5, 000 instructions which contain 250 branches, each of which skips over 8 instructions. Answer the following. a. How much faster is the pipelined machine over the non-pipelined machine assuming no branches are taken? b. How much faster is the pipelined machine over the non-pipelined machine assuming all branches are taken? c. Bonus question: Rather than 250 branches, assume there are b branches. How large would b have to be such that if all branches are taken, the pipelined machine and the non-pipelined machine have the same performance?

Explanation / Answer

a.

For Pipeline machine without branching :

number of instructions + (no. of stages-1) = 5011

For Non-Pipeline machine without branching :

No. of Instruction * no. of stages = 5000 * 12 = 60000

there fore pipelined machine is about 11.97 ~ 12 times faster.

b.

All branches taken,

Non pipelined : 5000*12 - 250*8*12 = 60000 - 24000 = 36000

Pipelined : 5011 - 250*8 = 5011-2000 = 3011

Pipelined will be about 11.95 ~ 12 times faster than non pipelined version

c.

no. of branches = b

speed of pipelined = speed of non pipelined

5011-b*8 = 60000 - b*8*12

11*b = 54989

b = 4999

there should be 4999 branches.

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