Software optimization can dramatically improve the performance of a computer sys

Question

Software optimization can dramatically improve the performance of a computer system. Assume that a CPU can perform a multiplication operation in 9ns and an addition or a subtraction in 1ns.

a. How long will it take for the CPU to calculate the result of following equation assuming that we only have 1 multiplier and 1 adder?

x = a * b * c * d + a * e b.

b. If possible, optimize the equation so that it takes less time. What is the best-case running time for the calculation of the equation? What if we have 2 multipliers and 1 adder?

Explanation / Answer

a)
Here there are 3 multiplications in a*b*c*d and 2 multiplications in a*e*b.
There is one addition.
So total time taken = 5*(9 ns) + 1*(1 ns) = 45+1 = 46ns

b)
X = a*b*c*d + a*e*b can be rewritten as X = a*b*(c*d + e)
There are 3 multiplications and 1 addition in new equation.

Hence total time taken = 3*9 + 1 = 27+1 = 28ns.

if there are two multipliers, then a*b and c*d can be performed parallelly.
Hence total time with 2 multipliers and 1 adder = 2*9 + 1 = 19ns.

if you have any doubts then you can ask in comment section.

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