A More Complex Example

Notes

• Assume that we have two different processors in the same family
  • This means that they have the same instruction set.
• However as we have seen, different instructions can have different CPIs
• So assume, that there are three different classes of instruction, with the following CPIs

  Processor\ Instruction Class	1	2	3
  PA	1	2	4
  PB	1	3	3

• Assume the following instruction mix:

  Processor\ Instruction Class Use	1	2	3
  PA	60%	20%	20%
  PB	50%	20%	30%

• We don't have a single CPI, but we can compute that.
• We will compute a Weighted Average
  • Let c_i be the CPI for class i∈{1,2,3}, (Table 1)
  • Let p_i be the Percent of time each instruction class is used (table 2)
  • $\text{CPI}_x = \sum_i c_i \times p_i$
  • $\text{CPI}_A = 1 \times .6 + 2 \times .2 + 4 \times .2 = 1.8$
  • $\text{CPI}_B = 1 \times .5 + 3 \times .2 + 3 \times .3 = 2.0$
• It is important to note that the weights (percent use) total 100%
  • We may have to compute these percents
    • P_A uses 4× 10⁵ instructions from class 1, 2× 10⁵ for class 2 and 1×10⁵ for class 3
      • We will use a total of (4 + 2 + 1) × 10⁵ or 7 × 10⁵ instructions.
      • Class 1 will be used 4/7 or about 57% of the time
      • Class 2 will be used 2/7 or about 29% of the time
      • Class 3 will be used 1/7 or about 14% of the time
      • Notice the total 100%
• So if instructions and IPS remain the same, CPU A will be better.
  • But what if, by changing the instruction execution percentage we either get fewer instructions, or can run the clock faster?
  • Ie assume that the clock speed remains constant, but

    Processor	Instruction Count
    PA	2.1×109
    PA	1.7×109

  • Each processor would need

                        c cycles
     n instructions x -------------  = n×c cycles
                      1 instruction 
    
    PA = 1.8 & times; 2.1 × 109 = 3.7 × 109 cycles
    PA = 2.0 & times; 1.7 × 109 = 3.4 × 109 cycles 

  • In this case, speeding up the third instruction class by changing the instruction count and mix would make a difference.
• Does it make sense that we can "tune" a cpu/circuit to perform some instructions better at the cost of other instructions?