Consider three different processors P1, P2, and P3 executing the same instruction set. P1 has a 3 GHz clock rate and a CPI of 1.5. P2 has a 2.5 GHz clock rate and a CPI of 1.0. P3 has a 4.0 GHz clock rate and has a CPI of 2.2.

a. Which processor has the highest performance expressed in instructions per second?

• tCPU_A = 10/20k, tCPU_B = 8/20k, tCPU_C = 11/20k ; k is constant, can be removed

  Performance는 B, A, C 순서

b. If the processors each execute a program in 10 seconds, find the number of cycles and the number of instructions.

• the number of cycle은 Freq, x 10s 하면 되고
• the number of instruction은 Total Cycle / CPI로 계산

c. We are trying to reduce the execution time by 30%, but this leads to an increase of 20% in the CPI. What clock rate should we have to get this time reduction?

• 실행 시간이 7/10이 되고, CPI는 12/10이 됨. 결국 위에 공식에 대입하면, 기존 Clock Cycle에서 12/7을 곱하면 구해짐.
• Freq_A = 5.14GHz, Freq_B = 4.29GHz, Freq_C = 6.86GHz

The Pentium 4 Prescott processor, released in 2004, had a clock rate of 3.6 GHz and voltage of 1.25 V. Assume that, on average, it consumed 10W of static power and 90 W of dynamic power. The Core i5 Ivy Bridge, released in 2012, has a clock rate of 3.4 GHz and voltage of 0.9 V. Assume that, on average, it consumed 30 W of static power and 40 W of dynamic power. a. For each processor find the average capacitive loads.

• Dynamic 기준으로 계산하면

  Prescott, 90W = Cload x 1.25^2 x 3.6G이므로 Ceff는 1.6nF

  Ivy Bridge, 40W = Cload x 0.9^2 x 3.4G이므로 Ceff는 1.45nF

b. Find the percentage of the total dissipated power comprised by static power and the ratio of static power to dynamic power for each technology.

• Prescott는 10W/100W = 10%, 비중은 0.11
• Ivy Bridge는 30W/70W = 42.86%, 비중은 0.75

c. If the total dissipated power is to be reduced by 10%, how much should the voltage be reduced to maintain the same leakage current?

Note: power is defined as the product of voltage and current.

• Power의 10% 감소는 V x I의 10% 감소인데, I를 고정하면 V가 10% 감소해야한다
• Prescott는 1.25V x 0.9 = 1.125V고, Ivy Bridge는 0.9V x 0.9 = 0.81V다

Assume a program requires the execution of 50 ×106 FP instructions, 110 ×106 INT instructions, 80 ×106 L/S instructions, and 16 ×106 branch instructions. The CPI for each type of instruction is 1, 1, 4, and 2, respectively. Assume that the processor has a 2 GHz clock rate. a. By how much must we improve the CPI of FP instructions if we want the program to run two times faster?

• #FP : 50 x 106, CPI: 1

• #INT: 110 x 106, CPI: 1

• #L/S: 80 x 106, CPI: 4

• #br: 16 x 106, CPI: 2

• Freq: 2GHz

• 1/2 = 50x + 110 + 320 + 32 / 50+110+320+32

  1/2 = 50x + 462 / 512 > 512 = 100x + 924고, x(개선된FP의 CPI) = -4.12…

b. By how much must we improve the CPI of L/S instructions if we want the program to run two times faster? c. By how much is the execution time of the program improved if the CPI of INT and FP instructions is reduced by 40% and the CPI of L/S and Branch is reduced by 30%?