Here is another realization of the fast exponentiation algorithm. Demonstrate that it is equivalent to the one
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Here is another realization of the fast exponentiation algorithm. Demonstrate that it is equivalent to the one in Figure 9.8.
1. \(\mathrm{f} \leftarrow 1 ; \mathrm{T} \leftarrow \mathrm{a} ; \mathrm{E} \leftarrow \mathrm{b}\)
2. if odd(e) then \(\mathrm{f} \leftarrow \mathrm{f} \times \mathrm{T}\)
3. \(\mathrm{E} \leftarrow[\mathrm{E} / 2]\)
4. \(\mathrm{T} \leftarrow \mathrm{T} \times \mathrm{T}\)
5. if \(\mathrm{E}>0\) then goto 2
6. output \(f\)
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