(thanks again for your response)
1) The source code is there  its complexity is only akin to say, rho method
2) My justification for claim of polynomial (ie logarithmic) speed:
a) [the second part of your original analysis] The number of steps required will tend to a constant (sic)
b) [the first part ditto] Each step can be performed in polynomial/logarithmic time using 'Russian Peasant' method of exponentiation
