  We present several new mathematical methods (ray-trace, inverse Fourier
transform and ellipse) and open-source software to compute the cdf, pdf and
inverse cdf of the generalized chi-square distribution. Some methods are geared
for speed, while others are designed to be accurate far into the tails, using
which we can also measure large values of the discriminability index d' between
multinormals. We characterize the performance and limitations of these and
previous methods, and recommend the best methods to use for each part of each
type of distribution. We also demonstrate the speed and accuracy of our new
methods against previous methods across a wide sample of distributions.
