Calculating the simple continued fraction of log(a)/log(b)

Calculating the simple continued fraction of log_ba

This performs an algorithm from T.H. Jackson and K.R. Matthews, On Shanks' algorithm for computing the continued fraction of log_ba, Journal of Integer Sequences 5 (2002) article 02.2.7.
We run the algorithm for c = b^r, r = m,...,n (suggested by Alan Offer).
Here a, b, m, n are positive integers satisfying a > b > 1, and 1 ≤ m ≤ n.
We find that if we add the restriction A_i,c > c + √c and A'_i,c > c + √c, we get better results, though this restriction does not seem to be needed when a = b+1.

With c = b^r, we have found that apart from some initial exceptional values of r, the correct partial quotients will be returned. In fact, if a=b+1, it seems that the correct partial quotients are always returned.
This is a BCMath version of the BC program log

Last modified 8th may 2018
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Calculating the simple continued fraction of logba

Calculating the simple continued fraction of log_ba