Addition chains?

Do you mean sequences that start at 1 and in which every term is the sum of two of the preceding terms?

How big is the target number? (just a rough order of magnitude)

What difference does the order of the number make?

Is there a general purpose algorithm, or is there one for big numbers, and one for small numbers.

From,
Nice coder

The repeated doubling until you create a term greater or equal to half of n, and then choosing the appropriate number of additional terms (given by the binary representation of n) gives you a means of having chains with length no longer than (2*log base 2 of n) - 1. Given that the obvious lower bound on the length of an addition chain is log n, you have the optimal length up to a constant factor.

ok, thanks.

How do i go and select the extra terms?

From,
Nice coder