RANDU

RANDU is Pseudorandom multiplicative congruential generator (MCG). This generator was first introduced in the early 1960s; its use soon became widespread during 1960's and 1970's. Its part of the IBM Scientific Subroutine Library for IBM System/360 computers.

RANDU uses MCG coeficients multiplier a = 65539 ( 2^16 + 3 ) and modulus m = 2^31 and constant c = 0. It can be implemented very quickly on 32-bit hardware in just 2 operations: wrapping multiplication by a and bit masking of result using AND 0x7fffffff.

Generated values are positive 31 bit integers. Generator period is 2^29. Lower bits have low randomness and should not be used separately. Problem with lower bits randomness and not achieving full period is common for all congruential generators with power of 2 modulus.

RANDU fails the spectral test for dimensions greater than 2. RANDU produces very strong banding when used in 3 dimensions. All points in 3d space fall in 15 two-dimensional planes. This effect can be used in GPU programming for visual effects and take advantage of compute simplicity.

References

https://en.wikipedia.org/wiki/RANDU

https://oeis.org/A096555

https://en.wikipedia.org/wiki/Linear_congruential_generator

Spectral test

Values 0.75 and higher are commonly considered as passing of the spectral test. While this generator failing higher dimensions it is a very strong in generating 2d data.

License

This is free and unencumbered software released into the public domain.

This code can be used under terms of CC0 or the Unlicense.