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68 lines
994 B
68 lines
994 B
2 years ago
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Exercise 1.16: Design a procedure that evolves
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an iterative exponentiation process that uses successive squaring and uses a
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logarithmic number of steps, as does fast-expt. (Hint: Using the
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observation that
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(
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b
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n
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2
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)
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2
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=
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(
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b
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2
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)
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n
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2
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, keep, along with
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the exponent
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n
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and the base
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b
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, an additional state variable
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a
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, and
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define the state transformation in such a way that the product
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a
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b
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n
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is unchanged from state to state. At the beginning of the process
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a
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is taken to be 1, and the answer is given by the value of
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a
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at the
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end of the process. In general, the technique of defining an
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invariant quantity that remains unchanged from state to state is a
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powerful way to think about the design of iterative algorithms.)
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