Random numbers

Abstract

Certain kinds of computations, such as sampling and simulation, need a source of random numbers. However, there are three significant problems when we try to compute such numbers:

• Numbers in computers, whether integer or floating-point, are rational numbers. Such numbers can only approximate mathematical real numbers, and therefore, truly random numbers cannot be produced by any computer algorithm.

• Most algorithms for generation of ‘random’ numbers produce a sequence of almost-always-different values that eventually repeats. The length of that sequence is called the period. By contrast, a stream of truly random numbers has occasional repetitions, and is never periodic.

• Software for random-number generation often contains subtle dependencies upon the behavior, precision, and range of integer and floating-point arithmetic.

Any one who considers arithmetical methods of producing random numbers is, of course, in a state of sin.

— John von Neumann (1951).

A random number generator chosen at random isn’t very random.

— Donald E. Knuth.