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How about a closed form evaluation?
F(n) = (Phi^n - (1-Phi)^n) / sqrt(5)
Where Phi is the Golden Ratio.
Phi = (1 + sqrt(5)) / 2
In that case, you'll need phi and sqrt(5) to have enough precision to round correctly. For the 1000th Fibonacci number, you'd need both to have over 200 digits of accuracy. You then have to take your large (data-wise) decimal number and take it to a large power. Computationally, it would be much worse than repeated addition.
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