The Ziggurat Method for Generating Random Variables

Abstract

We provide a new version of our ziggurat method for generating a random variable from a given decreasing density. It is faster and simpler than the original, and will produce, for example, normal or exponential variates at the rate of 15 million per second with a C version on a 400MHz PC. It uses two tables, integers k_i, and reals w_i. Some 99% of the time, the required x is produced by: Generate a random 32-bit integer j and let i be the index formed from the rightmost 8 bits of j. If j < k, return x = j x w_i.

We illustrate with C code that provides for inline generation of both normal and exponential variables, with a short procedure for settting up the necessary tables.