Spigot algorithm and reliable computation of natural logarithm (Q701962)

For details on the spigot algorithm the author refers to his previous paper [ibid. 7, No.3, 247-273 (2001; Zbl 0986.65052)], on root computing. For the logarithm, the procedure is based on the decomposition \(\ln Q= k \times \ln 2+\ln(1+p/q)\), with \(p\) and \(q\) positive integers, \(p<q\). Means for determining an upper bound for the biggest integer occurring in the process of spigot computing are provided.