  Monte Carlo simulation is an important tool for modeling highly nonlinear
systems (like particle colliders and cellular membranes), and random,
floating-point numbers are their fuel. These random samples are frequently
generated via the inversion method, which harnesses the mapping of the quantile
function Q(u) (e.g. to generate proposal variates for rejection sampling). Yet
the increasingly large sample size of these simulations makes them vulnerable
to a flaw in the inversion method; Q(u) is ill-conditioned in a distribution's
tails, stripping precision from its sample. This flaw stems from limitations in
machine arithmetic which are often overlooked during implementation (e.g. in
popular C++ and Python libraries). This paper introduces a robust inversion
method, which reconditions Q(u) by carefully drawing and using uniform
variates. pqRand, a free C++ and Python package, implements this novel method
for a number of popular distributions (exponential, normal, gamma, and more).
