I was reading some university material, and I found that to calculate the CPI (clock cycles per instruction) of a CPU, we use the following formula:
CPI = Total execution cycles / executed instructions count
this is clear and does make sense, but for this example it says that n instructions have been executed:
instruction type frequency relative CPI
1 50% 3
2 20% 4
3 30% 5
why is the total CPI equal to 3*0.5+4*0.2+5*0.3 = 3.8 and not 3.8/3 = 1.26 because following the above formula, there are a total of 3 executed instructions, or am I understanding the formula in a wrong way?
The formula is correct but you are not reading the table right.
instruction type frequency relative CPI
1 50% 3
2 20% 4
3 30% 5
The first line means you have an instruction that uses 3 CPI and this instruction has a frequency of 50% which basically means every second instruction in your program is this instruction.
Instruction 2 needs 4 CPI to be executed but occurs only 20% in your program. Instruction 3 needs 5 CPI but occurs 30%.
Therefore you calculate 0.5 * 3 + 0.2 * 4 + 0.3 + 5 = 3.8.
It is basically the average CPI.
Just imagine you have following program:
INS_1 3 CPI
INS_3 5 CPI
INS_1 3 CPI
INS_3 5 CPI
INS_2 4 CPI
INS_1 3 CPI
INS_3 5 CPI
INS_2 4 CPI
INS_1 3 CPI
INS_1 3 CPI
--------------
38 CPI / 10 (Instructions) = 3.8