  The cumulative distribution and quantile functions for the one-sided one
sample Kolmogorov-Smirnov probability distributions are used for
goodness-of-fit testing. While the Smirnov-Birnbaum-Tingey formula for the CDF
appears straight forward, its numerical evaluation generates intermediate
results spanning many hundreds of orders of magnitude and at times requires
very precise accurate representations. Computing the quantile function for any
specific probability may require evaluating both the CDF and its derivative,
both of which are computationally expensive. To work around avoid these issues,
different algorithms can be used across different parts of the domain, and
approximations can be used to reduce the computational requirements. We show
here that straight forward implementation incurs accuracy loss for sample sizes
of well under 1000. Further the approximations in use inside the open source
SciPy python software often result in increased computation, not just reduced
accuracy, and at times suffer catastrophic loss of accuracy for any sample
size. Then we provide alternate algorithms which restore accuracy and
efficiency across the whole domain.
