Sampling exactly from the normal distribution

TL;DR

This paper presents an exact sampling algorithm for the normal distribution that uses only simple integer operations, enabling precise, efficient generation of normal deviates without floating point arithmetic.

Contribution

It introduces a novel algorithm that samples exactly from the normal distribution using only integer operations, with linear cost in precision and adaptability to discrete normal distributions.

Findings

Generates normal deviates exactly rounded to any precision.

Operates without floating point or transcendental functions.

Cost scales linearly with the desired precision.

Abstract

An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in the same base. Thereafter, uniform random digits are copied directly into the representation of the normal deviate. Thus, in contrast to existing methods, it is possible to generate normal deviates exactly rounded to any precision with a mean cost that scales linearly in the precision. The method performs no extended precision arithmetic, calls no transcendental functions, and, indeed, uses no floating point arithmetic whatsoever; it uses only simple integer operations. It can easily be adapted to sample exactly from the discrete normal distribution whose parameters are rational numbers.