An operation can be speeded up by applying two different optimizations, O1 and O2. These optimizations operate on different parts of the process and there is no overlap. If O1 speeds up fraction f1 of the program by S1 and O2 speeds up fraction f2 of the program by S2, what is the overall speedup?
What will be an ideal response?
The time taken to perform the operation is f1 + f2 + (1 ? f1 ? f2) when no speedup is applied.
With speedup, the time is f1/S1 + f2/S2 + (1 ? f1 ? f2) because the two fractions are speeded up.
The speedup ratio between the unmodified and modified task is 1/( f1/S1 + f2/S2 + (1 ? f1 ? f2)). This assumes that
there is no overlap between the portions f1 and f2.
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