  The cumulative distribution and quantile functions for the two-sided one
sample Kolmogorov-Smirnov probability distributions are used for
goodness-of-fit testing. The CDF is notoriously difficult to explicitly
describe and to compute, and for large sample size use of the limiting
distribution is an attractive alternative, with its lower computational
requirements. No closed form solution for the computation of the quantiles is
known. Computing the quantile function by a numeric root-finder for any
specific probability may require multiple evaluations of both the CDF and its
derivative. Approximations to both the CDF and its derivative can be used to
reduce the computational demands. We show that the approximations in use inside
the open source SciPy python software result in increased computation, not just
reduced accuracy, and cause convergence failures in the root-finding. Then we
provide alternate algorithms which restore accuracy and efficiency across the
whole domain.
