Nope, that's not a problem. You don't need a closed form and simple equation to build the lookup table (inverse CDF). Use whatever expensive and iterative fun

Nope, that's not a problem. You don't need a closed form and simple equation to build the lookup table (inverse CDF). Use whatever expensive and iterative functions you want to build it. For the normal distribution, you can use a bisection on the math.h erf() function to invert it. This is expensive, but you're only going to do it to make your lookup table once. Build that table to reasonably fit in your cache, and then use your uniform pseudo random integers to peak into that table. As I mentioned above, you can interpolate between values in the table if you need more resolution. There are other tricks for specific distributions, but the technique is very general.