The algorithms for both versions of the power function given in this chapter are rather simpleminded. Is it really necessary to make eight multiplications to compute x8? It can be observed that x8 = (x4)2, x4 = (x2)2, and x2 = x · x; that is, only three multiplications are needed to find the value of x8. Using this observation, improve both algorithms for computing xn. Hint: A special case is needed for odd exponents.
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