Efficient table-free sampling methods for the exponential, Cauchy, and normal distributions

Three algorithms for sampling from exponential, Cauchy and normal distributions are developed. They are based on the "exact approximation" method, and their expected numbers of consumed uniform deviates are less than 1.04 per sample from the target distributions. The algorithms are simple and easily implemented in any desired precision. They require no space for long tables of auxiliary vectors, merely a few constants are needed. Nevertheless, their speed compares well with the performance of much more complex and table-aided sampling procedures.