Amdahl’s law can be applied in contexts other than parallel processing. Suppose that a

Numerical application consists of 20% floating-point and 80% integer/control operations (these are based on operation counts rather than their execution times). The execution time of a floating-point operation is three times as long as other operations. We are considering a redesign of the floating-point unit in a microprocessor to make it faster.

a. Formulate a more general version of Amdahl’s law in terms of selective speed-up of a portion of a computation rather than in terms of parallel processing.

b. How much faster should the new floating-point unit be for 25% overall speed improvement?

c. What is the maximum speed-up that we can hope to achieve by only modifying the floating-point unit?