For the following questions, assume that for a given program 70% of the executed

Question

For the following questions, assume that for a given program 70% of the executed instructions are arithmetic, 10% are load/store, and 20% are branch. a. Given this instruction mix and the assumption that an arithmetic instruction requires two cycles, a load/store instruction takes six cycles, and a branch instruction takes three cycles, find the average CPI. b. For a 25% improvement in performance, how many cycles, on average, may an arithmetic instruction take if load/store and branch instructions are not improved at all? c. For a 50% improvement in performance, how many cycles, on average, may an arithmetic instruction take if load/store and branch instructions are not improved at all?

Explanation / Answer

Arthimetic instructions ---> 70%
Load/Store --> 10%
Branches --> 20%

a) Given ,

Operation |Frequency | Clock cycles

------------------------------------------------------

Arthimetic | 70% | 2
Load/Store | 10% | 6
Branches | 20% | 3

CPI (old) = 0.70 + 0.10 + 0.20 = 1
CPI (new) = (0.70 * 2) + (0.10 * 6) + (0.20 * 3)
   = 1.4 + 0.6 + 0.6
   = 2.6
CPI average = (1 + 2.6)/2 = (3.6)/2 = 1.8

b) We need to get 25% improvement in performance.

Assume, you have 100 operators : 70 Arthimatic, 10 Load/store and 20 Branches. You want to reduce the number of arthimatic instructions until you have only 75 operators left. Because their is no change in load/store and Branch instructions at all.

Now, How many arthimatic instructions do we have = 70 - 25 = 45 operators i.e, 45% ---> Arthimatic instructions has to be executed.

c) We need to get 50% improvement in performance.

Assume, you have 100 operators : 70 Arthimatic, 10 Load/store and 20 Branches. You want to reduce the number of arthimatic instructions until you have only 50 operators left. Because their is no change in load/store and Branch instructions at all.

Now, How many arthimatic instructions do we have = 70 - 50 = 20 operators i.e, 20% ---> Arthimatic instructions has to be executed.

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