If your p-values are approaching machine precision then you don't need better floating point precision you need to be using the log-likelihood (admittedly for g

If your p-values are approaching machine precision then you don't need better floating point precision you need to be using the log-likelihood (admittedly for gaussian samples this is the variance which requires some careful handling). Also if your p-values are approaching machine precision, then maybe p-values aren't the most meaningful metric.