We perform the algorithm of J.L. Davison, An algorithm for the continued fraction of ep/m, Proceedings of the Eighth Manitoba Conference on Numerical Mathematics and Computing (Univ. Manitoba, Winnipeg, 1978), 169-179, Congress. Numer., XXII, Utilitas Math.
The starting point is a result of R.F.C. Walters in Alternate derivation of some regular continued fractions, J. Austr. Math. Soc 8 (1968), 205-212): If
then pn/rn and qn/sn → ep/m.
We first find the least n=n* such that pn, qn, rn, sn are non-negative and repeatedly apply Raney's factorisation for n*≤ k ≤ n*+N, as in Davison's example in §3.
The number (count) of partial quotients of ep/q found is returned.
We cannot predict the value of count, but it becomes positive for sufficiently large N.
We restrict taking p/q no greater than 14, because of the time taken to compute a0 for larger values of p/q.
This is a BCMATH translation of a BC program.
A faster C version is available.
Inside the program, p and q are replaced by p/gcd(p,q) and q/gcd(p,q).
Last modified 7th August 2017
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