Search

In 2016, Karney proposed an exact sampling algorithm for the standard normal distribution. In this paper, we study the computational complexity of this algorithm under the random deviate model. Specifically, Karney's algorithm requires the access to an infinite sequence of independently and uniformly random deviates over the range (0,1). We give an estimate of the expected number of uniform deviates used by this algorithm until outputting a sample value, and present an improved algorithm with lower uniform deviate consumption. The experimental results also shows that our improved algorithm has better performance than Karney's algorithm.

Xorshift128+ are pseudo random number generators with eight sets of parameters. Some of them are standard generators in many platforms, such as JavaScript V8 Engine. We show that in the 3D plots generated by this method, points concentrate on planes, ruining the randomness.

Xorshift128+ is a newly proposed pseudorandom number generator (PRNG), which is now the standard PRNG on a number of platforms. We demonstrate that three-dimensional plots of the random points generated by the generator have visible structures: they concentrate on particular planes in the cube. We provide a mathematical analysis of this phenomenon.