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Suppose you have a machine that executes a program consisting of 40% floating point multiply, 30%...

  1. Suppose you have a machine that executes a program consisting of 40% floating point multiply, 30% floating point divide, and the remaining 30% are from other instructions. Management wants you to make the machine 2x faster. You can make the multiply operation 10x faster OR the divide 4x faster. Can you meet management’s goal by making ONE improvement? If so, which one?
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Answer #1

Given that Program instructions consists of :

  • 40% floating point multiply
  • 30% floating point divide
  • 30% other instructions

Amdahl's law states that:

Assuming initially that floating point multiply, divide and other instructions have same clocks per instruction (CPI).

New execution time after improvement with multiply = (40) / 10 + (30 + 30) = 64

New execution time after improvement with Divide = (30) / 4 + (40 + 30) = 77.5

New execution time after improvement with multiply and divide = (40 / 10) + (30 / 4) + 30 = 41.5

New system should be 2x faster which means new execution time should be below = 100/ 2 = 50.

Therefore, Management's goal can NOT be achieved by making the improvement with Multiply or divide alone. However it can be achieved by making both improvements at a time.

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