Question

Assume that for a given program 70% of the executed instructions are arithmetic, 10% are load/store, and 20% are branch.

2.47.1 [5] <§2.19> Given this instruction mix and the assumption that an

arithmetic instruction requires 2 cycles, a load/store instruction takes 6 cycles, and a branch instruction takes 3 cycles, find the average CPI.

2.47.2 [5] <§2.19> 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?

2.47.3 [5] <§2.19> 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?

Short answer

2.47.1

The average cycle per instruction is 2.6.

2.47.2

There are 1.95 cycles on average.

2.47.3

There are 1.3 cycles on average.

Step-by-step solution

Define the concept.

2.47.1

$$\begin{gathered} TheaverageCPI=\left[\right(Numberofrequiredcycleforthearitmeticinstruction\times thepercentageoftheexecutedarithmeticinstructions) \\ +(Numberofrequiredcycleforloadorstoreinstruction\times thepercentageoftheexecutedloadorstoreinstructions) \\ +(Numberofrequiredcycleforthebranchinstruction\times thepercentageoftheexecutedbranchinstructions\left)\right] \end{gathered}$$

2.47.2

$TheaverageCPI=CP{I}_{previous}\times \left(\frac{100-thepercentageofimprovementinperformance}{100}\right)$

2.47.3

$TheaverageCPI=CP{I}_{previous}\times \left(\frac{100-thepercentageofimprovementinperformance}{100}\right)$

Determine the calculation.

2.47.1

Given, the percentage of the executed arithmetic instructions is 70%,10% for the load or store, and 20% for the branch.

Also given that,

2 cycles are required for the arithmetic instruction.

6 cycles are required for the load/store instruction.

And 3 cycles are required for the branch instruction.

$$\begin{gathered} HencetheaverageCPI=(2\times 0.7)+(6\times 0.1)+(3\times 0.2) \\ =1.4+0.6+0.6=2.6 \end{gathered}$$

2.47.2

Given that the percentage of improvement in performance is 25%.

The previous average CPI is 2.6.

So, the average CPI = 2.6 x 0.75 = 1.95

Hence, there are 1.95 cycles on average.

2.47.3

Given that the percentage of improvement in performance is 50%.

The previous average CPI is 2.6.

So, the average CPI = 2.6 x 0.50 = 1.3

Hence, there are 1.3 cycles on average