Complete the following questions on CPU performance and show

Complete the following questions on CPU performance and show all of your work.

1. Suppose you wish to run a program P with 3 x 109 instructions on a 4.5 GHz machine with a CPI of 1.8. What is the expected CPU time?

2. Suppose you have the following instruction mix. What is the CPI?

Instruction Type Frequency Cycles

Memory 27 2

ALU 40 1

Branch 25 2

Jump 8 1

3. Consider two different processors P1 and P2 executing the same instruction set with the clock rates and CPIs given in the following table.

a. If the processors each execute a program in 15 seconds, find the number of cycles and the number of instructions for each processor.

b. We are trying to reduce the program execution time by 25%, but this leads to an increase of 20% in the CPI. What clock rate should we have to get this time reduction for each processor?

Processor Clock Rate CPI

P1 4 GHz 2

P2 4.5 GHz 1.5

You may find this table of clock cycle times and clock rates useful:

Solution

1. CPU time= instruction count (IC)* clocks per instruction (CPI)* clock time (CT)

Here,

IC= 3*10^9

CPI=1.8

CT=1/4.5*10^9=0.22*10^-9

Expected CPU time=(3*10^9)*(1.8)*(0.22*10^-9)=1.188 s

2. CPI=Summation of (freq./100*cycles)

CPI=0.27*2+0.40*1+0.25*2+0.08*1=1.52

CPI=1.52

3. a. Number of cycles=CPU clock rate*execution time

P1=4*10^9*15=6*10^10

P2=4.5*10^9*15=6.75*10^10

Number of instructions=CPU clock rate*execution time/CPI

P1=4*10^9*15/2=3*10^10

P2=4.5*10^9*15/1.5=4.5*10^10

b. Execution time=(Number of instructions*CPI)/(clock rate)

We have to reduce the program execution time by 25% and increase 20% of CPI

Execution time*0.75=(Number of instructions*CPI*1.2)/(clock rate)

New clock rate=Old clock rate*1.2/0.75=old clock rate*1.6

New clock rate

P1=4*1.6*10^9=6.4*10^9

P2=4.5*1.6*10^9=7.2*10^9